Blockchain Papers

Steven Dryall

FinTECH Circle, London, UK

Stjepan Begušić, Zvonko Kostanjčar, H. Eugene Stanley, Boris Podobnik

Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting findings, such as the inverse cubic law in the tails of stock price fluctuation distributions. Motivated by the rise of novel digital assets based on blockchain technology, we study the distributions of cryptocurrency price fluctuations. We consider Bitcoin returns over various time intervals and from multiple digital exchanges, in order to investigate the existence of universal scaling behavior in the tails, and ascertain whether the scaling exponent supports the presence of a finite second moment. We provide empirical evidence on slowly decaying tails in the distributions of returns over multiple time intervals and different exchanges, corresponding to a power-law. We estimate the scaling exponent and find an asymptotic power-law behavior with 2 < α < 2.5 suggesting that Bitcoin returns, in addition to being more volatile, also exhibit heavier tails than stocks, which are known to be around 3. Our results also imply the existence of a finite second moment, thus providing a fundamental basis for the usage of standard financial theories and covariance-based techniques in risk management and portfolio optimization scenarios.

Simon Shadman, Linus Roxbergh

Studiens syfte är att undersöka om uppmätt sentiment på Twitter kan vara en förutsägande faktor för priset på Bitcoin. En kvantitativ undersökning genomförs med regressionsmodeller där data inhämtas från Twitter i realtid. Resultatet indikerar ett svagt samband där bäst resultat erhölls med en tidsfördröjning av sentiment på 16 timmar, vilket tyder på att det kan finnas möjligheter att använda Twitter för att förutspå förändringar av priset på Bitcoin. Variationen av resultat för olika tidsperioder gör dock att det är svårt att dra generella slutsatser av studien.

Leonardo Ermann, Klaus M. Frahm, Dima L. Shepelyansky

We construct and study the Google matrix of Bitcoin transactions during the time period from the very beginning in 2009 till April 2013. The Bitcoin network has up to a few millions of bitcoin users and we present its main characteristics including the PageRank and CheiRank probability distributions, the spectrum of eigenvalues of Google matrix and related eigenvectors. We find that the spectrum has an unusual circle-type structure which we attribute to existing hidden communities of nodes linked between their members. We show that the Gini coefficient of the transactions for the whole period is close to unity showing that the main part of wealth of the network is captured by a small fraction of users.

Francisco Prieto‐Castrillo, Sergii Kushch, Juan M. Corchado

This work presents a theoretical and numerical analysis of the conditions under which distributed sequential consensus is possible when the state of a portion of nodes in a network is perturbed. Specifically, it examines the consensus level of partially connected blockchains under failure/attack events. To this end, we developed stochastic models for both verification probability once an error is detected and network breakdown when consensus is not possible. Through a mean field approximation for network degree we derive analytical solutions for the average network consensus in the large graph size thermodynamic limit. The resulting expressions allow us to derive connectivity thresholds above which networks can tolerate an attack.

Alexander Elgart, A. Klein, Günter Stolz

Abstract We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mstyle> </mml:math> XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in Elgart et al (2018 J. Funct. Anal . (in press)). This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb–Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.

Joshua Skewes, Dorthe Døjbak Håkonsson, Trine Bilde, Andreas Roepstorff

Collaborative decision making is central to the organization of society. Juries deliberate cases, voters elect government officials, open innovation networks converge on innovative solutions. It is common to think of such groups as decision making entities. But this language is imprecise. Real decision processes do not occur within any group or organization as an abstract entity. Collaborative decision making happens within and between autonomous individuals. This emphasizes the importance of the relationships between individual and social decision-making processes to social organization. Despite a rich body of literature on collaborative decision making we know little about how individuals decide to commit to group decision making in the first place, and how, once joined, they communicate their distributed information for optimal group performance. We introduce a general framework designed to model collaborative decision processes. Our main results are that 1) commitment and gain is enhanced when groups are designed so agents have realistic knowledge about the forgone gains and losses associated with abstaining from the group; and 2) that this effect is accelerated when communication between group members conveys more information about individual preferences. We thus demonstrate that collaborative decision making is done best when it is done by groups that are informationally open.

Alessandra Cretarola, Gianna Figg-Talamanca, Marco Patacca

In recent literature it is claimed that BitCoin price behaves more likely to a volatile stock asset than a currency and that changes in its price are influenced by sentiment about the BitCoin system itself; in Kristoufek [10] the author analyses transaction based as well as popularity based potential drivers of the BitCoin price finding positive evidence. Here, we endorse this finding and consider a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as a second factor, affecting the price itself, which represents a sentiment indicator. We prove that the suggested model is arbitrage-free under a mild condition and, based on risk-neutral evaluation, we obtain a closed formula to approximate the price of European style derivatives on the BitCoin. By applying the same approximation technique to the joint likelihood of a discrete sample of the bivariate process, we are also able to fit the model to market data. This is done by using both the Volume and the number of Google searches as possible proxies for the sentiment factor. Further, the performance of the pricing formula is assessed on a sample of market option prices obtained by the website deribit.com.

Mattia Bongini, Massimo Fornasier

In recent years, numerous studies have focused on the mathematical modeling of social dynamics, with self-organization, i.e., the autonomous pattern formation, as the main driving concept. Usually, first or second order models are employed to reproduce, at least qualitatively, certain global patterns (such as bird flocking, milling schools of fish or queue formations in pedestrian flows, just to mention a few). It is, however, common experience that self-organization does not always spontaneously occur in a society. In this review chapter we aim to describe the limitations of decentralized controls in restoring certain desired configurations and to address the question of whether it is possible to externally and parsimoniously influence the dynamics to reach a given outcome. More specifically, we address the issue of finding the sparsest control strategy for finite agent-based models in order to lead the dynamics optimally towards a desired pattern.

Kaj-Kolja Kleineberg, Dirk Helbing

Abstract A multidimensional financial system could provide benefits for individuals, companies, and states. Instead of top-down control, which is destined to eventually fail in a hyperconnected world, a bottom-up creation of value can unleash creative potential and drive innovations. Multiple currency dimensions can represent different externalities and thus enable the design of incentives and feedback mechanisms that foster the ability of complex dynamical systems to self-organize and lead to a more resilient society and sustainable economy. Modern information and communication technologies play a crucial role in this process, as Web 2.0 and online social networks promote cooperation and collaboration on unprecedented scales. Within this contribution, we discuss how one dimension of a multidimensional currency system could represent socio-digital capital (Social Bitcoins) that can be generated in a bottom-up way by individuals who perform search and navigation tasks in a future version of the digital world. The incentive to mine Social Bitcoins could sustain digital diversity, which mitigates the risk of totalitarian control by powerful monopolies of information and can create new business opportunities needed in times where a large fraction of current jobs is estimated to disappear due to computerization.

Marie Larsson Linton, Ernie G. S. Teo, Elisabeth Bommes, Cheng–Ying Chen · 5 authors

No abstract is available for this record.

Sören Adamsson, Muhammad Hammad Nadeem Tahir

This study analyses the growing area of research that explores the evolution of technology from social and cognition perspective – and how the design and various implementation of technology are being shaped by the factors related to social-constructivism and beliefs systems of individuals. The newly developed technological phenomena of Cryptocurrency – the digital currency for all, provides us with an excellent case to study. We apply social and cognitive processes to understand technology trajectories across the life cycle of cryptocurrency. We thus deepen our understanding by analyzing why and what causes the various technological trajectories in the era of ferment and concluding our research by deriving various technological 'themes'. – that might evolve as the phenomena of cryptocurrency while moving towards the era of dominant design.

G. N. Vinogradova

The main subject of this thesis is a paradigm of instability and stabilization in coalition forming among countries as rational actors, presented through a Statistical Physics inspired model.This is an interdisciplinary work involving the fields of applied mathematics and sociophysics, as well as the political applications in the real cases from past and present. Applied to political,economic and social problems, the models can be used to analyze a wide variety of real cases -- international alliances, economic or business alliances, coalitions of political parties, socialnetworks, and organizational structures.In the first part of this thesis we present and analyze the coalition forming and the instability among rational actors coupled with pairwise static historical propensity bonds that have evolvedindependently. Such organization leads to discordant associations into coalitions and the instability as a consequence of decentralized maximization of the individual benefits gained fromjoining or leaving the coalitions. We define Natural Model of coalition forming and address the questions of instability and stabilization among actors possessing different levels of rationality. The framework presented here allows to analytically calculate the optimal and non-optimal stable configurations of actors' coalitions. We then investigate the coalition forming and the stabilization under the influence of externally-set opposing global alliances, which are represented in Global Alliance Model. The stabilization is produced through new cooperations based on the effect of polarization of several distinct interests shared by actors, which generates interest-based propensities and enables a planned coalition forming. We then investigate the effect of dissolution of a global alliancewhich, together with the competing alliance, has previously generated stable coalitions.A special section of the thesis is devoted to investigation and illustration of coalition forming in real historical cases. This part presents the analysis of unstable coalitions in Europe - cycling in the England-Spain-France conflicting triangle and creation of the Italian state, as well as of the remarkable historical cases of the Soviet global alliance collapse, of the recent internal conflict in Syria, and of the "paradoxical stability" in the Eurozone.In the second part of this thesis, we present a simulation of the coalition forming models. The simulation allows to follow graphically the coalition forming processes. We present the methodology used in the simulation, as well as its application in the illustration of coalition forming in the prototypes of real case systems. Given exact propensity values, which is fairly consideredto be the most difficult part of coalition forming modeling, the simulation tool can be used to predict optimal and non-optimal spontaneous stabilizations and globally motivated stabilities inreal cases.An independent part of the thesis is devoted to the subject of viability correction in dynamic network of actors. The model is a finite set of autonomous actors with states that evolveindependently and connected into a network via their connection operators, which evolve independently as well. The network is defined to be viable if a joint evolution satisfies the centralized scarcity constraints set by the environment. In order to restore the viability of these decentralized dynamics, we apply to the method of correction by viability multipliers used in Viability Theory, where the multipliers play the role of decentralizing prices. Standing apart from the main course of the thesis, the subject of viability correction in dynamic network of actors suggests an interesting theoretic dynamical generalization of coalition stabilization in our models inspired from Statistical Physics.

Dániel Kondor, Márton Pósfai, István Csabai, Gábor Vattay

The possibility to analyze everyday monetary transactions is limited by the scarcity of available data, as this kind of information is usually considered highly sensitive. Present econophysics models are usually employed on presumed random networks of interacting agents, and only macroscopic properties (e.g. the resulting wealth distribution) are compared to real-world data. In this paper, we analyze BitCoin, which is a novel digital currency system, where the complete list of transactions is publicly available. Using this dataset, we reconstruct the network of transactions, and extract the time and amount of each payment. We analyze the structure of the transaction network by measuring network characteristics over time, such as the degree distribution, degree correlations and clustering. We find that linear preferential attachment drives the growth of the network. We also study the dynamics taking place on the transaction network, i.e. the flow of money. We measure temporal patterns and the wealth accumulation. Investigating the microscopic statistics of money movement, we find that sublinear preferential attachment governs the evolution of the wealth distribution. We report a scaling relation between the degree and wealth associated to individual nodes.

Jing Huang, Bo Yang, Di Jin, Yi Yang

No abstract is available for this record.

Marco LiCalzi, Andrea Collevecchio

Abstract. We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a partition generated by a random scheme consistent with his cognitive capacity. Assuming that agents ’ partitions are independently distributed, we prove that the asymptotic probability of nontrivial common knowledge undergoes a phase transition. Regardless of the number of agents, when their cognitive capacity is sufficiently large, the probability goes to one; and when it is small, it goes to zero. Our proofs rely on a graph-theoretic characterization of common knowledge that has independent interest.

Jasmina Omić

Epidemic theory has wide range of applications in computer networks, from spreading of malware to the information dissemination algorithms. Our society depends more strongly than ever on such computer networks. Many of these networks rely to a large extent on decentralization and self-organization. While decentralization removes obvious vulnerabilities related to single points of failure, it leads to a higher complexity of the system. A more complex type of vulnerability appears in such systems. For instance, computer viruses are imminent threats to all computer networks. We intend to study the interaction between malware spreading and strategies that are designed to cope with them. The main goals of this thesis are: 1. to analyze influence of network topology on infection spread 2. to determine how topology can be used for network protection 3. to formulate and study optimization of malware protection problem with respect to topology 4. to investigate non-cooperative game of security We used analytical tools from various fields to answer these questions. First of all, we have developed homogeneous and heterogeneous N-intertwined, susceptible - infected - susceptible (SIS) model for virus spread. This model is used to determine the influence of topology on the spreading process. For the N-intertwined model, we show that the largest eigenvalue of the adjacency matrix of the graph rigorously defines the epidemic threshold. The results of the model also predict the upper and lower bounds on epidemics as a function of nodal degree. The epidemic threshold is found to be a consequence of the mean field approximation. However, slow convergence to the steady-state justifies the application of the threshold concept. We used the exact 2N-state Markov chain model to explore the phase transition phenomenon for two contrasting cases, namely the line graph and the complete graph. The N-intertwined model assumes that the infection spreading over a link is a Poisson process. By introducing infection delay, we studied the influence of deviation from Poisson process assumption on epidemic threshold for the special case of a complete bi-partite graph. Due to the special structure of bi-partite graphs we were also able to derive approximate formula for the extinction probability in the first phase of the infection. In the case of SIS epidemic models, the effects of infection depend on the protection of individual nodes. We studied optimization of protection scheme for different networks. We use the results from heterogeneous N-intertwined model to determine the global optimum at the threshold. Above the threshold, the problem is a sum of ratios fractional programming problem, which is NP-complete. Therefore, we only determine the upper bound on the optimum. Contrary to the common sense, reducing the probability of infection for higher degree nodes pushes the network out of the global optimum. For the case of complete bi-partite graphs, we derive optimal threshold if only 2 fixed protection rates are available. Computer networks are generally distributed systems and protection cannot be globally optimized. The Internet is an extreme example: there is no global control center, and obtaining complete information on its global state is an illusion. To approach the issue of security over decentralized network, we derived a novel framework for network security under the presence of autonomous decision makers. The problem under the consideration is the N players non-cooperative game. We have established the existence of a Nash equilibrium point (NEP). The willingness of nodes to invest in protection depends on the price of protection. We showed that, when the price of protection is relatively high for all the nodes, the only equilibrium point is that of a completely unprotected network; while if this price is sufficiently low for a single node, it will always invest in protecting itself. We determine bounds on the Price of Anarchy (PoA), that describes how far the NEP is from the global optimum. We have also proposed two methods for steering the network equilibrium, namely by influencing the relative prices and by imposing an upper bound on infection probabilities. A quarantine is another possible measure against the epidemic. A quarantine on a set of network nodes separates them from the rest of the network by removing links. The concept of threshold and the N-intertwined model provides a tool to analyze how quarantine improves the network protection. We studied several different networks from artificially generated to real-world examples using the modularity algorithm. The real-world networks tend to show a better epidemic threshold after clustering than artificially generated graphs. The real-world networks have typically two or three big clusters and several smaller ones, while Barabasi-Albert (BA) and Erdos-Renyi (ER) graphs have several smaller clusters comparable in size. However, the number of removed links in a graph using modularity algorithm is unjustifiably high, suggesting that complete quarantine is not a viable solution for real-world networks.

Stuart M. Allen, Gualtiero B. Colombo, Roger M. Whitaker

We address the problem of cooperation in decentralized systems, specifically looking at interactions between independent pairs of peers where mutual exchange of resources (e.g., updating or sharing content) is required. In the absence of any enforcement mechanism or protocol, there is no incentive for one party to directly reciprocate during a transaction with another. Consequently, for such decentralized systems to function, protocols for self-organization need to explicitly promote cooperation in a manner where adherence to the protocol is incentivized. In this article we introduce a new generic model to achieve this. The model is based on peers repeatedly interacting to build up and maintain a dynamic social network of others that they can trust based on similarity of cooperation. This mechanism effectively incentivizes unselfish behavior, where peers with higher levels of cooperation gain higher payoff. We examine the model's behavior and robustness in detail. This includes the effect of peers self-adapting their cooperation level in response to maximizing their payoff, representing a Nash-equilibrium of the system. The study shows that the formation of a social network based on reflexive cooperation levels can be a highly effective and robust incentive mechanism for autonomous decentralized systems.