Nicolò Vallarano, Matteo Bruno, Emiliano Marchese, Giuseppe Di Trapani · 8 authors
Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant patterns in graphs, counting networked configurations with given properties. From a technical point of view, the ERGMs workflow is defined by two subsequent optimization steps: the first one concerns the maximization of Shannon entropy and leads to identify the functional form of the ensemble probability distribution that is maximally non-committal with respect to the missing information; the second one concerns the maximization of the likelihood function induced by this probability distribution and leads to its numerical determination. This second step translates into the resolution of a system of $O(N)$ non-linear, coupled equations (with $N$ being the total number of nodes of the network under analysis), a problem that is affected by three main issues, i.e. accuracy, speed and scalability. The present paper aims at addressing these problems by comparing the performance of three algorithms (i.e. Newton's method, a quasi-Newton method and a recently-proposed fixed-point recipe) in solving several ERGMs, defined by binary and weighted constraints in both a directed and an undirected fashion. While Newton's method performs best for relatively little networks, the fixed-point recipe is to be preferred when large configurations are considered, as it ensures convergence to the solution within seconds for networks with hundreds of thousands of nodes (e.g. the Internet, Bitcoin). We attach to the paper a Python code implementing the three aforementioned algorithms on all the ERGMs considered in the present work.
In the blockchain network, to get rewards in the blockchain, blockchain participants pay for various forms of competition such as computing power, stakes, and other resources. Because of the need to pay a certain cost, individual participants cooperate to maintain the long‐term stability of the blockchain jointly. In the course of such competition, the game between each other has appeared invisibly. To better understand the blockchain design of cooperation mechanisms, in this paper, we constructed a game framework between participants with different willingness, using evolutionary game theory, and complex network games. We analyzed how the behavior of participants potentially develops with cost and payoff. We consider the expected benefits of participants for the normal growth of the blockchain as the major factor. Considering the behavior of malicious betrayers, the blockchain needs to be maintained in the early stage. Numerical simulation supports our analysis.
Blockchain and general purpose distributed ledgers are foundational technologies which bring significant innovation in the infrastructures and other underpinnings of our socio-economic systems. These P2P technologies are able to securely diffuse information within and across networks, without need for trustees or central authorities to enforce consensus. In this contribution, we propose a minimalistic stochastic model to understand the dynamics of blockchain-based consensus. By leveraging on random-walk theory, we model block propagation delay on different network topologies and provide a classification of blockchain systems in terms of two emergent properties. Firstly, we identify two performing regimes: a functional regime corresponding to an optimal system function; and a non-functional regime characterised by a congested or branched state of sub-optimal blockchains. Secondly, we discover a phase transition during the emergence of consensus and numerically investigate the corresponding critical point. Our results provide important insights into the consensus mechanism and sub-optimal states in decentralised systems.
The usage of cryptocurrencies, together with that of financial automated consultancy, is widely spreading in the last few years. However, automated consultancy services are not yet exploiting the potentiality of this nascent market, which represents a class of innovative financial products that can be proposed by robo-advisors. For this reason, we propose a novel approach to build efficient portfolio allocation strategies involving volatile financial instruments, such as cryptocurrencies. In other words, we develop an extension of the traditional Markowitz model which combines Random Matrix Theory and network measures, in order to achieve portfolio weights enhancing portfolios' risk-return profiles. The results show that overall our model overperforms several competing alternatives, maintaining a relatively low level of risk.
Shahar Somin, Goren Gordon, Alex Pentland, Erez Shmueli · 5 authors
Following the birth of Bitcoin and the introduction of the Ethereum ERC20 protocol a decade ago, recent years have witnessed a growing number of cryptographic tokens that are being introduced by researchers, private sector companies and NGOs. The ubiquitous of such Blockchain based cryptocurrencies give birth to a new kind of rising economy, which presents great difficulties to modeling its dynamics using conventional semantic properties. Our work presents the analysis of the dynamical properties of the ERC20 protocol compliant crypto-coins' trading data using a network theory prism. We examine the dynamics of ERC20 based networks over time by analyzing a meta-parameter of the network, the power of its degree distribution. Our analysis demonstrates that this parameter can be modeled as an under-damped harmonic oscillator over time, enabling a year forward of network parameters predictions.
Bitcoin-otc is a peer to peer (over-the-counter) marketplace for trading with bitcoin crypto-currency. To mitigate the risks of the p2p unsupervised exchanges, the establishment of a reliable reputation systems is needed: for this reason, a web of trust is implemented on the website. The availability of all the historic of the users' interaction data makes this dataset a unique playground for studying reputation dynamics through others' evaluations. We analyze the structure and the dynamics of this web of trust with a multilayer network approach distinguishing the rewarding and the punitive behaviors. We show that the rewarding and the punitive behavior have similar emergent topological properties (apart from the clustering coefficient being higher for the rewarding layer) and that the resultant reputation originates from the complex interaction of the more regular behaviors on the layers. We show that the systems' reputation inequality reaches a high steady value with the network evolution. We characterize the reputation trajectories identifying prototypical behaviors associated to three classes of users: trustworthy, untrusted and controversial. Controversial users are the only ones presenting up and down reputation trends. We focus on these cases for understanding which are the possible factors driving reputation falls and which dynamical patterns characterize these cascades: some users have real oscillating behaviors, other abuse of the trust system doing a few good transactions to gain reputation for cheating the users afterwards, other naturally and slowly die out after a long series of positive exchanges (like disappearing from the system) and finally, some users are hardly beaten by organized trolling attacks.
Vladimir Soloviev, Symon P. Yevtushenko, Viktor Batareyev
This article demonstrates the comparative possibility of constructing indicators of critical and crash phenomena in the volatile market of cryptocurrency and developed stock market. Then, combining the empirical cross-correlation matrix with the Random Matrix Theory, we mainly examine the statistical properties of cross-correlation coefficients, the evolution of the distribution of eigenvalues and corresponding eigenvectors in both markets using the daily returns of price time series. The result has indicated that the largest eigenvalue reflects a collective effect of the whole market, and is very sensitive to the crash phenomena. It has been shown that introduced the largest eigenvalue of the matrix of correlations can act like indicators-predictors of falls in both markets.
Andrey Pogudin, Anindya S. Chakrabati, Tiziana Di Matteo
Cryptocurrencies represent an asset class featuring two unique properties: they are not backed by sovereigns, and their supply is fixed exogenously. This combination becomes apparent in their volatility, which is driven only by demand-side factors. In particular, cryptocurrencies represent an extreme case of the excess volatility puzzle, with asset prices moving more than the fundamentals. We explore the effects of market capitalization on the dynamics of cryptocurrencies within both returns and volatility networks and show that these cryptocurrencies exhibit scaling properties in volatility with respect to market capitalization. The dependency network suggests that currencies with a larger market share have a larger presence in the dominant eigenspectrum, and they exert more influence in the comovement network. In these regards, we find parallels between the dynamics of cryptocurrencies and those of more traditional asset classes. Our findings have implications for both researchers and practitioners in terms of modeling and analyzing the collective behavior of financial assets.
Diogo Pacheco, Pik-Mai Hui, Christopher Torres-Lugo, Bao Tran Truong · 6 authors
Coordinated campaigns are used to influence and manipulate social media platforms and their users, a critical challenge to the free exchange of information online. Here we introduce a general, unsupervised network-based methodology to uncover groups of accounts that are likely coordinated. The proposed method constructs coordination networks based on arbitrary behavioral traces shared among accounts. We present five case studies of influence campaigns, four of which in the diverse contexts of U.S. elections, Hong Kong protests, the Syrian civil war, and cryptocurrency manipulation. In each of these cases, we detect networks of coordinated Twitter accounts by examining their identities, images, hashtag sequences, retweets, or temporal patterns. The proposed approach proves to be broadly applicable to uncover different kinds of coordination across information warfare scenarios.
Decentralized Finance is the new socioeconomic system growing with an extremely fast pace and changing the way financial interactions are being conducted. In comparison with the growing importance of digital assets and blockchain technology, there is still little understanding of Decentralized Finance as a system. In this thesis we analyze transaction datasets from Bitcoin and Ethereum blockchains to obtain a comprehensive understanding of digital assets -from studying the behaviour of each part to investigating the whole structure and deriving the relations between micro and macro properties of the cryptocurrency systems. Using the Complex Networks approach we explained the system's overall structure and dynamics, and uncovered the mechanism behind network formation. It was found that there is fitness preferential attachment among nodes in the bitcoin network that leads the system to scale-free behaviour. We proposed the quantifiable definition of fitness and supported our finding by simulating a synthetic network and reproducing the main properties of the bitcoin network. After having a good understanding about the structure of the system, we zoom in into its parts by studying the behavioral patterns among the system's users (people). We develop the methodology based on Machine Learning models to define distinct behavioral types in the cryptocurrency systems and find that despite differences between the bitcoin and ethereum systems, there are four common strategies that users follow in both markets. Based on our finding, we model the dynamics of people's behaviour in market as an Absorbing Markov Chain. This approach allowed us to present the behavioral switches in a comprehensive and intuitive way. Moreover, we were able to obtain the predictions on the longevity of users in the system according to their behaviour. Finally, we use the Granger causality test to derive the relations between all system characteristics. We attempt to explain the effect of behavioral switches on the structural properties and price; we find that indeed, switches of users from certain behavioral groups causes a change in price which affects the size of the network as well. We hope that the work and results presented in this thesis will advance the understanding of the new field of Decentralized Finance and expect that the research approach and methodologies developed for this study will be helpful to investigate various complex systems as well.
Vladimir Soloviev, Сергій Олексійович Семеріков, Victoria Solovieva
The informational (Kolmogorov) measure of complexity in accordance with the Lempel-Ziv algorithm (LZC) is calculated for the logarithmic returns of daily Bitcoin/$ values. The calculations were carried out for a moving window with a variation in its size (50–250 days) in increments of one day in the framework of the implemented coarse graining procedure. It is shown that in both mono-and multi-scaling versions, LZC is sensitive to noticeable fluctuations in the Bitcoin price that occur as a result of critical events in the cryptocurrency market. In equilibrium, stable state, having a relatively low value, LZC rapidly increases immediately before the crisis, which proves the dominance of the chaotic component of the time series. The classification and periodization of crisis phenomena in the cryptocurrency market for the period 2010–2020 has been carried out. The results demonstrate the possibility of using the LZC measure as an indicator-precursor of crisis phenomena in the cryptocurrency market.
Ioannis Chalkiadakis, Anna Zaremba, Gareth W. Peters, Michael J. Chantler
This paper establishes a new framework for assessing multimodal statistical causality between cryptocurrency market (cryptomarket) sentiment and cryptocurrency price processes. In order to achieve this, we present an efficient algorithm for multimodal statistical causality analysis based on Multiple-Output Gaussian Processes. Signals from different information sources (modalities) are jointly modelled as a Multiple-Output Gaussian Process, and then using a novel approach to statistical causality based on Gaussian Processes (GPs), we study linear and non-linear causal effects between the different modalities. We demonstrate the effectiveness of our approach in a machine learning application by studying the relationship between cryptocurrency spot price dynamics and sentiment time-series data specific to the crypto sector, which we conjecture influences retail investor behaviour. The investor sentiment is extracted from cryptomarket news data via methods developed in the area of statistical machine learning known as Natural Language Processing (NLP). To capture sentiment, we present a novel framework for text to time-series embedding, which we then use to construct a sentiment index from publicly available news articles. We conduct a statistical analysis of our sentiment statistical index model and compare it to alternative state-of-the-art sentiment models popular in the NLP literature. In regard to the multimodal causality, the investor sentiment is our primary modality of exploration, in addition to price and a blockchain technology-related indicator (hash rate). Analysis shows that our approach is effective in modelling causal structures of variable degree of complexity between heterogeneous data sources and illustrates the impact that certain modelling choices for the different modalities can have on detecting causality. A solid understanding of these factors is necessary to gauge cryptocurrency adoption by retail investors and provide sentiment- and technology-based insights about the cryptocurrency market dynamics.
We study the liquid democracy problem, where each voter can either directly vote to a candidate or delegate his voting power to a proxy. We consider the implementation of liquid democracy on the blockchain through Ethereum smart contract and to be compatible with the realtime self-tallying property, where the contract itself can record ballots and update voting status upon receiving each voting massage. A challenge comes due to the gas fee limitation of Ethereum mainnet, that the number of instruction for processing a voting massage can not exceed a certain amount, which restrict the application scenario with respect to algorithms whose time complexity is linear to the number of voters. We propose a fast algorithm to overcome the challenge, such that i) shifts the on-chain initialization to off-chain and ii) the on-chain complexity for processing each voting massage is O(\log n), where n is the number of voters.
Ayana T. Aspembitova, Ling Feng, Valentin Melnikov, Lock Yue Chew
Bitcoin is the earliest cryptocurrency and among the most successful ones to date. Recently, its dynamical evolution has attracted the attention of the research community due to its completeness and richness in historical records. In this paper, we focus on the detailed evolution of bitcoin trading with the aim of elucidating the mechanism that drives the formation of the bitcoin transaction network. Our empirical investigation reveals that although the temporal properties of the transaction network possesses scale-free degree distribution like many other networks, its formation mechanism is different from the commonly assumed models of degree preferential attachment or wealth preferential attachment. By defining the fitness value of each node as the ability of the node to attract new connections, we have instead uncovered that the observed scale-free degree distribution results from the intrinsic fitness of each node following a power-law distribution. Our finding thus suggests that the "good-get-richer" rather than the "rich-get-richer" paradigm operates within the bitcoin ecosystem. Based on these findings, we propose a model that captures the temporal generative process by means of a fitness preferential attachment and data-driven birth/death mechanism. Our proposed model is able to produce structural properties in good agreement with those obtained from the empirical bitcoin network.
Cryptocurrencies are a novel and disruptive technology that has prompted a new approach to how currencies work in the modern economy. As such, online discussions related to cryptocurrencies often go beyond posts about the technology and underlying architecture of the various coins, to subjective speculations of price fluctuations and predictions. Furthermore, online discussions, potentially driven by foreign adversaries, criminals or hackers, can have a significant impact on our economy and national security if spread at scale.
In September 2018 the authors released a report funded by the Law Foundation entitled “Regulation of Cryptocurrencies in New Zealand”. This article includes the report’s recommendations as well as background on the implications of cryptocurrencies and blockchain to society and the law.
Cryptocurrencies, in particular bitcoin, have captured the public’s attention. It is hard to find a person who has not heard about bitcoin, albeit blockchain, the technology that the creators of bitcoin devised, is still a mystery to most. Blockchain, however, is just one form of distributed ledger technology (DLT). For the sake of simplicity, the term blockchain is used in this article.
The blockchain technology promises to transform finance, money and even governments. However, analyses of blockchain applicability and robustness typically focus on isolated systems whose actors contribute mainly by running the consensus algorithm. Here, we highlight the importance of considering trustless platforms within the broader ecosystem that includes social and communication networks. As an example, we analyse the flash-crash observed on 21st June 2017 in the Ethereum platform and show that a major phenomenon of social coordination led to a catastrophic cascade of events across several interconnected systems. We propose the concept of ``emergent centralisation'' to describe situations where a single system becomes critically important for the functioning of the whole ecosystem, and argue that such situations are likely to become more and more frequent in interconnected socio-technical systems. We anticipate that the systemic approach we propose will have implications for future assessments of trustless systems and call for the attention of policy-makers on the fragility of our interconnected and rapidly changing world.
Gengxin Sun, Sheng Bin, Meng Jiang, Ning Cao · 8 authors
With the emergence and development of blockchain technology, a new type of social networks based on blockchain had emerged. In these social networks high quality content creators, filters and propagators can all be reasonably motivated. Due to the transparency and traceability brought by blockchain technology, the public opinion propagation in such social networks presents new characteristics and laws. Based on the theory of network propagation and blockchain, a new public opinion propagation model for this kind of social network based on blockchain technology is proposed in this paper. The model considers the effect of incentive mechanism produced by reasonably quantifying value contribution on the propagation of information in such social networks, and the income-risk matrix under different propagation behaviors is constructed. Furthermore, the transformation process and transfer probability among different states in the propagation model are defined on the basis of income-risk matrix. The model is helpful to break the bottleneck of network public opinion management by using blockchain technology. The propagation of false network public opinion can be contained, and a good ecological environment of network public opinion propagation would be realized.
This article demonstrates the possibility of constructing indicators of critical and crash phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex networks have been used. The possibility of constructing dynamic measures of network complexity behaving in a proper way during actual pre-crash periods has been shown. This fact is used to build predictors of crashes and critical events phenomena on the examples of all the patterns recorded in the time series of the key cryptocurrency Bitcoin, the effectiveness of the proposed indicators-precursors of these falls has been identified.
Anton Kolonin, Ben Goertzel, Deborah Duong, Matthew Iklé · 5 authors
Understanding the principles of consensus in communities and finding ways to optimal solutions beneficial for entire community becomes crucial as the speeds and scales of interaction in modern distributed systems increase. Such systems can be both social and information computer networks that unite the masses of people as well as multi-agent computing platforms based on peer-to-peer interactions including those operating on the basis of distributed ledgers. It is now becoming possible for hybrid ecosystems to emerge, having such systems including both humans and computer systems using artificial intelligence. We propose a new form of consensus for all of the listed systems, based on the reputation of the participants, calculated according to the principle of liquid democracy. We believe that such a system will be more resistant to social engineering and reputation manipulation than the existing systems. In this article, we discuss the basic principles and options for implementing such a system, and also present preliminary practical results.
The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that the bitcoin price exhibits a very interesting multi-scale correlation structure. This structure can be described by a power-law behavior of the variances of the returns as functions of time increments and it can be characterized by two parameters, the volatility and the Hurst exponent. These power-law parameters, however, vary in time. A new notion of generalized Hurst exponent is introduced which allows us to check if the multi-fractal character of the underlying signal is well captured. It is moreover shown how the monitoring of the power-law parameters can be used to identify regime shifts for the bitcoin price. A novel technique for identifying the regimes switches based on a goodness of fit of the local power-law parameters is presented. It automatically detects dates associated with some known events in the bitcoin market place. A very surprising result is moreover that, despite the wild ride of the bitcoin price in recent years and its multi-fractal and non-stationary character, this price has both local power-law behaviors and a very orderly correlation structure when it is observed on its entire period of existence.
Cryptocurrency is a well-developed blockchain technology application that is currently a heated topic throughout the world. The public availability of transaction histories offers an opportunity to analyze and compare different cryptocurrencies. In this paper, we present a dynamic network analysis of three representative blockchain-based cryptocurrencies: Bitcoin, Ethereum, and Namecoin. By analyzing the accumulated network growth, we find that, unlike most other networks, these cryptocurrency networks do not always densify over time, and they are changing all the time with relatively low node and edge repetition ratios. Therefore, we then construct separate networks on a monthly basis, trace the changes of typical network characteristics (including degree distribution, degree assortativity, clustering coefficient, and the largest connected component) over time, and compare the three. We find that the degree distribution of these monthly transaction networks cannot be well fitted by the famous power-law distribution, at the same time, different currency still has different network properties, e.g., both Bitcoin and Ethereum networks are heavy-tailed with disassortative mixing, however, only the former can be treated as a small world. These network properties reflect the evolutionary characteristics and competitive power of these three cryptocurrencies and provide a foundation for future research.
Aurelio F. Bariviera, Luciano Zunino, Osvaldo A. Rosso
This paper discusses the dynamics of intraday prices of twelve cryptocurrencies during last months' boom and bust. The importance of this study lies on the extended coverage of the cryptoworld, accounting for more than 90\% of the total daily turnover. By using the complexity-entropy causality plane, we could discriminate three different dynamics in the data set. Whereas most of the cryptocurrencies follow a similar pattern, there are two currencies (ETC and ETH) that exhibit a more persistent stochastic dynamics, and two other currencies (DASH and XEM) whose behavior is closer to a random walk. Consequently, similar financial assets, using blockchain technology, are differentiated by market participants.