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Blockchain-based systems are frequently governed through tokens that grant their holders voting rights over core protocol functions and funds. The centralisation occurring in Decentralised Finance (DeFi) protocols' token-based voting systems is typically analysed by examining token holdings' distribution across addresses. In this paper, we expand this perspective by exploring shared token holdings of addresses across multiple DeFi protocols. We construct a Statistically Validated Network (SVN) based on shared governance token holdings among addresses. Using the links within the SVN, we identify influential addresses that shape these connections and we conduct a post-hoc analysis to examine their characteristics and behaviour. Our findings reveal persistent influential links over time, predominantly involving addresses associated with institutional investors who maintain significant token supplies across the sampled protocols. Finally, we observe that token holding patterns and concentrations tend to shift in response to speculative market cycles.

In this paper we describe a prototype of a blockchain-in-a-box system which allows users to easily bootstrap the whole Ethereum Proof-of-Work (PoW) network running on multiple Raspberry Pi nodes - an inexpensive modular computers. Users are able to orchestrate the whole blockchain network using a single web based interface, for example they are able to set the topology of the peer-to-peer (P2P) connections and control the initialization parameters. Each Raspberry Pi has a screen attached which visualizes current state of local blockchain, allowing users to easily visualize the consensus of the network in real time. We show how this platform can be used to perform experiments on consensus quality while using different P2P topologies. Similar experiments can be used for demonstration purposes in a workshop or other educational settings.

ChainScience 2024, the second edition of the interdisciplinary conference, brought together academics, practitioners, and industry experts to explore novel developments in the realm of distributed ledger technologies. The conference aimed to bridge diverse fields such as informatics, business, economics, finance, regulation, law, mathematics, physics, and complexity science. The papers presented in these conference proceedings address emerging topics such as AI/ML applications to blockchain, DLTs interoperability, decentralized financial services, and tokenomics, alongside ethical, societal, and governance aspects of blockchain and DLTs. With a focus on promoting high-quality research and interdisciplinary collaboration, ChainScience24 aimed to unlock the collective potential of its diverse participants, embodying the ethos that the whole is greater than the sum of its parts.

Ethereum 2.0, as the preeminent smart contract blockchain platform, guarantees the precise execution of applications without third-party intervention. At its core, this system leverages the Proof-of-Stake (PoS) consensus mechanism, which utilizes a stochastic process to select validators for block proposal and validation, consequently rewarding them for their contributions. However, the implementation of blockchain technology often diverges from its central tenet of decentralized consensus, presenting significant analytical challenges. Our study collects consensus reward data from the Ethereum Beacon chain and conducts a comprehensive analysis of reward distribution and evolution, categorizing them into attestation, proposer and sync committee rewards. To evaluate the degree of decentralization in PoS Ethereum, we apply several inequality indices, including the Shannon entropy, the Gini Index, the Nakamoto Coefficient, and the Herfindahl-Hirschman Index (HHI). Our comprehensive dataset is publicly available on Harvard Dataverse, and our analytical methodologies are accessible via GitHub, promoting open-access research. Additionally, we provide insights on utilizing our data for future investigations focused on assessing, augmenting, and refining the decentralization, security, and efficiency of blockchain systems.

When considering a specific event, news that accurately reflects the ground truth is deemed as real information, while news that deviates from the ground truth is classified as false information. False information often spreads fast due to its novel and attention-grabbing content, which poses a threat to our society. By extending the Susceptible-Infected (SI) model, our research offers analytical decision boundaries that enable effective interventions to get desirable results, even when intermediate functions cannot be analytically solved. These analytical results may provide valuable insights for policymakers in false information control. When assessing intervention costs using the model, the results indicate that the sooner we intervene, the lower the overall intervention cost tends to be.

IOTA is a distributed ledger technology that relies on a peer-to-peer (P2P) network for communications. Recently an auto-peering algorithm was proposed to build connections among IOTA peers according to their "Mana" endowment, which is an IOTA internal reputation system. This paper's goal is to detect potential vulnerabilities and evaluate the resilience of the P2P network generated using IOTA auto-peering algorithm against eclipse attacks. In order to do so, we interpret IOTA's auto-peering algorithm as a random network formation model and employ different network metrics to identify cost-efficient partitions of the network. As a result, we present a potential strategy that an attacker can use to eclipse a significant part of the network, providing estimates of costs and potential damage caused by the attack. On the side, we provide an analysis of the properties of IOTA auto-peering network ensemble, as an interesting class of homophile random networks in between 1D lattices and regular Poisson graphs.

An important virtue of distributed ledger technologies is their acclaimed higher level of decentralisation compared to traditional financial systems. Empirical literature, however, suggests that many systems tend towards centralisation as well. This study expands the current literature by offering a first-time, data-driven analysis of the degree of decentralisation of the platform Hedera Hashgraph, a public permissioned distributed ledger technology, employing data directly fetched from a network node. The results show a considerably higher amount of released supply compared to the release schedule and a growing number of daily active accounts. Also, Hedera Hashgraph exhibits a high centralisation of wealth and a shrinking core that acts as an intermediary in transactions for the rest of the network. However, the Nakamoto index and Theil index point to recent progress towards a more decentralised network.

The open availability of the entire history of the Bitcoin transactions opens up the possibility to study this system at an unprecedented level of detail. This contribution is devoted to the analysis of the mesoscale structural properties of the Bitcoin User Network (BUN), across its entire history (i.e. from 2009 to 2017). What emerges from our analysis is that the BUN is characterized by a core-periphery structure a deeper analysis of which reveals a certain degree of bow-tieness (i.e. the presence of a Strongly-Connected Component, an IN- and an OUT-component together with some tendrils attached to the IN-component). Interestingly, the evolution of the BUN structural organization experiences fluctuations that seem to be correlated with the presence of bubbles, i.e. periods of price surge and decline observed throughout the entire Bitcoin history: our results, thus, further confirm the interplay between structural quantities and price movements observed in previous analyses., Comment: 17 pages, 11 figures

The proceedings of ChainScience 2023 epitomize the integration of various scientific disciplines with the dynamic world of blockchain and AI. This collection, encapsulating both full and short papers, as well as posters, delves into areas such as cryptoeconomics, machine learning, and analysis of blockchain networks, under the guiding principle of this year's conference: 'Applying insights and methods from the physical, mathematical, behavioral, and computational sciences to blockchain and the future of AI'. This diverse compilation offers a critical examination of theoretical constructs and innovative practical applications to empower the future of the blockchain industry., Comment: Held 15-17 June 2023 in Boston, Massachusetts, USA

This paper presents a study of the Poof-of-Stake (PoW) Ethereum consensus protocol, following the recent switch from Proof-of-Work (PoS) to Proof-of-Stake within Merge upgrade. The new protocol has resulted in reduced energy consumption and a shift in economic incentives, but it has also introduced new threat sources such as chain reorganizations and balancing attacks. Using a simple and flexible agent-based model, this study employs a time-continuous simulation algorithm to analyze the evolution of the blocktree and assess the impact of initial conditions on consensus quality. The model simulates validator node behavior and the information propagation throughout the peer-to-peer network of validators to analyze the resulting blockchain structure. Key variables in the model include the topology of the peer-to-peer network and average block and attestation latencies. Metrics to evaluate consensus quality are established, and means to observe the model's responsiveness to changes in parameters are provided. The simulations reveal a phase transition in which the system switches from a consensus state to a non-consensus state, with a theoretical justification presented for this observation., Comment: 8 pages, 4 figures

The behaviour of Bitcoin owners is reflected in the structure and the number of bitcoin transactions encoded in the Blockchain. Likewise, the behaviour of Bitcoin traders is reflected in the formation of bullish and bearish trends in the crypto market. In light of these observations, we wonder if human behaviour underlies some relationship between the Blockchain and the crypto market. To address this question, we map the Blockchain to a spin-lattice problem, whose configurations form ordered and disordered patterns, representing the behaviour of Bitcoin owners. This novel approach allows us to obtain time series suitable to detect a causal relationship between the dynamics of the Blockchain and market trends of the Bitcoin and to find that disordered patterns in the Blockchain precede Bitcoin panic selling. Our results suggest that human behaviour underlying Blockchain evolution and the crypto market brings out a fascinating connection between disorder and panic in Bitcoin dynamics., Comment: 6 pages, 3 figures

The core of many cryptocurrencies is the decentralised validation network operating on proof-of-work technology. In these systems, validation is done by so-called miners who can digitally sign blocks once they solve a computationally-hard problem. Conventional wisdom generally considers this protocol as secure and stable as miners are incentivised to follow the behaviour of the majority. However, whether some strategic mining behaviours occur in practice is still a major concern. In this paper we target this question by focusing on a security threat: a selfish mining attack in which malicious miners deviate from protocol by not immediately revealing their newly mined blocks. We propose a statistical test to analyse each miner's behaviour in five popular cryptocurrencies: Bitcoin, Litecoin, Monacoin, Ethereum and Bitcoin Cash. Our method is based on the realisation that selfish mining behaviour will cause identifiable anomalies in the statistics of miner's successive blocks discovery. Secondly, we apply heuristics-based address clustering to improve the detectability of this kind of behaviour. We find a marked presence of abnormal miners in Monacoin and Bitcoin Cash, and, to a lesser extent, in Ethereum. Finally, we extend our method to detect coordinated selfish mining attacks, finding mining cartels in Monacoin where miners might secretly share information about newly mined blocks in advance. Our analysis contributes to the research on security in cryptocurrency systems by providing the first empirical evidence that the aforementioned strategic mining behaviours do take place in practice.

Ranking the spreading influence of nodes is of great importance in practice and research. The key to ranking a node's spreading ability is to evaluate the fraction of susceptible nodes been infected by the target node during the outbreak, i.e., the outbreak size. In this paper, we present a dynamic Markov process (DMP) method by integrating the Markov chain and the spreading process to evaluate the outbreak size of the initial spreader. Following the idea of the Markov process, this method solves the problem of nonlinear coupling by adjusting the state transition matrix and evaluating the probability of the susceptible node being infected by its infected neighbours. We have employed the susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) models to test this method on real-world static and temporal networks. Our results indicate that the DMP method could evaluate the nodes' outbreak sizes more accurately than previous methods for both single and multi-spreaders. Besides, it can also be employed to rank the influence of nodes accurately during the spreading process.

More than ten years ago the blockchain was acclaimed as the solution to overcome centralised trusted third parties for online payments. Through the years the crypto-movement changed and evolved, although decentralisation remained the core ideology and the necessary feature every new crypto-project should provide. In this paper we study the concept of centralisation in cryptocurrencies using a wide array of methodologies from the complex systems literature, on a comparative collection of blockchains, in order to define the many different levels a blockchain system may display (de-)centralisation and to question whether the present state of cryptocurrencies is, in a technological and economical sense, actually decentralised.

We propose a novel framework to analyse the velocity of money in terms of the contribution (MicroVelocity) of each individual agent, and to uncover the distributional determinants of aggregate velocity. Leveraging on complete publicly available transactions data stored in blockchains from four cryptocurrencies, we empirically find that MicroVelocity i) is very heterogeneously distributed and ii) strongly correlates with agents' wealth. We further document the emergence of high-velocity intermediaries, thereby challenging the idea that these systems are fully decentralised. Further, our framework and results provide policy insights for the development and analysis of digital currencies.

The Bitcoin Lightning Network (BLN) was launched in 2018 to scale up the number of transactions between Bitcoin owners. Although several contributions concerning the analysis of the BLN binary structure have recently appeared in the literature, the properties of its weighted counterpart are still largely unknown. The present contribution aims at filling this gap, by considering the Bitcoin Lightning Network over a period of 18 months, ranging from 12th January 2018 to 17th July 2019, and focusing on its weighted, undirected, daily snapshot representation. As the study of the BLN weighted structural properties reveals, it is becoming increasingly 'centralised' at different levels, just as its binary counterpart: 1) the Nakamoto coefficient shows that the percentage of nodes whose degrees/strengths 'enclose' the 51% of the total number of links/total weight is rapidly decreasing; 2) the Gini coefficient confirms that several weighted centrality measures are becoming increasingly unevenly distributed; 3)the weighted BLN topology is becoming increasingly compatible with a core-periphery structure, with the largest nodes 'by strength' constituting the core of such a network, whose size keeps shrinking as the BLN evolves. Further inspection of the resilience of the weighted BLN shows that removing such hubs leads to the network fragmentation into many components, an evidence indicating potential security threats - as the ones represented by the so called 'split attacks'., Comment: 18 pages, 12 figures

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.

Bitcoin is built on a blockchain, an immutable decentralised ledger that allows entities (users) to exchange Bitcoins in a pseudonymous manner. Bitcoins are associated with alpha-numeric addresses and are transferred via transactions. Each transaction is composed of a set of input addresses (associated with unspent outputs received from previous transactions) and a set of output addresses (to which Bitcoins are transferred). Despite Bitcoin was designed with anonymity in mind, different heuristic approaches exist to detect which addresses in a specific transaction belong to the same entity. By applying these heuristics, we build an Address Correspondence Network: in this representation, addresses are nodes are connected with edges if at least one heuristic detects them as belonging to the same entity. %addresses are nodes and edges are drawn between addresses detected as belonging to the same entity by at least one heuristic. %nodes represent addresses and edges model the likelihood that two nodes belong to the same entity %In this network, connected components represent sets of addresses controlled by the same entity. In this paper, we analyse for the first time the Address Correspondence Network and show it is characterised by a complex topology, signalled by a broad, skewed degree distribution and a power-law component size distribution. Using a large-scale dataset of addresses for which the controlling entities are known, we show that a combination of external data coupled with standard community detection algorithms can reliably identify entities. The complex nature of the Address Correspondence Network reveals that usage patterns of individual entities create statistical regularities; and that these regularities can be leveraged to more accurately identify entities and gain a deeper understanding of the Bitcoin economy as a whole., Comment: 21 pages, 13 figures

Originally a speculative pattern in ecological networks, the hybrid or compound nested-modular pattern has been confirmed, during the last decade, as a relevant structural arrangement that emerges in a variety of contexts --in ecological mutualistic system and beyond. This implies shifting the focus from the measurement of nestedness as a global property (macro level), to the detection of blocks (meso level) that internally exhibit a high degree of nestedness. Unfortunately, the availability and understanding of the methods to properly detect in-block nested partitions lie behind the empirical findings: while a precise quality function of in-block nestedness has been proposed, we lack an understanding of its possible inherent constraints. Specifically, while it is well known that Newman-Girvan's modularity, and related quality functions, notoriously suffer from a resolution limit that impairs their ability to detect small blocks, the potential existence of resolution limits for in-block nestedness is unexplored. Here, we provide empirical, numerical and analytical evidence that the in-block nestedness function lacks a resolution limit, and thus our capacity to detect correct partitions in networks via its maximization depends solely on the accuracy of the optimization algorithms., Comment: 12 pages, 4 figures, 1 table

The Bitcoin Lightning Network (BLN), a so-called "second layer" payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the three representations above, we find that the total volume of transacted bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin Lightning Network) is, in fact, ~0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the Undirected Binary Configuration Model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks., Comment: 11 pages, 7 figures

Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion, different mathematical definitions of nestedness have been proposed, sometimes giving contrasting results. Moreover, there is an ongoing debate on the statistical significance of nestedness, since even random networks where the number of connections (degree) of each node is fixed to its empirical value are typically as nested as real-world ones. Here we propose a clarification that exploits the recent finding that random networks where the degrees are enforced as hard constraints (microcanonical ensembles) are thermodynamically different from random networks where the degrees are enforced as soft constraints (canonical ensembles). We show that if the real network is perfectly nested, then the two ensembles are trivially equivalent and the observed nestedness, independently of its definition, is indeed an unavoidable consequence of the empirical degrees. On the other hand, if the real network is not perfectly nested, then the two ensembles are not equivalent and alternative definitions of nestedness can be even positively correlated in the canonical ensemble and negatively correlated in the microcanonical one. This result disentangles distinct notions of nestedness captured by different metrics and highlights the importance of making a principled choice between hard and soft constraints in null models of ecological networks., Comment: 16 pages, 12 figures

Can we predict top-performing products, services, or businesses by only monitoring the behavior of a small set of individuals? Although most previous studies focused on the predictive power of "hub" individuals with many social contacts, which sources of customer behavioral data are needed to address this question remains unclear, mostly due to the scarcity of available datasets that simultaneously capture individuals' purchasing patterns and social interactions. Here, we address this question in a unique, large-scale dataset that combines individuals' credit-card purchasing history with their social and mobility traits across an entire nation. Surprisingly, we find that the purchasing history alone enables the detection of small sets of ``discoverers" whose early purchases offer reliable success predictions for the brick-and-mortar stores they visit. In contrast with the assumptions by most existing studies on word-of-mouth processes, the hubs selected by social network centrality are not consistently predictive of success. Our findings show that companies and organizations with access to large-scale purchasing data can detect the discoverers and leverage their behavior to anticipate market trends, without the need for social network data., Comment: Main text (pp. 1-13), Online appendix (pp. 14-34)

Mass Media outlets have occupied the central role of the political scenario, and are persuasive in the process of opinion formation of the citizens. In particular, the study of the relationship between Mass Media and behaviour of citizens can be monitored during election times, given the accessibility of news related to the candidates and polls that precede the election's day. In this paper we present a novel two-dimensional data driven Mass Media model based on semantic analysis of newspapers and national election surveys, which we use to analyse how a single influence mechanism should behave in order to reproduce the behaviour of the voters. Using simple and feasible rules for dynamics, we were able to find a notable agreement between the model's predictions and the polls which help us to understand the underlying mechanisms of the interactions between reader and media.

Cryptocurrencies are distributed systems that allow exchanges of native tokens among participants, or the exchange of such tokens for fiat currencies in markets external to these public ledgers. The availability of their complete historical bookkeeping opens up the possibility of understanding the relationship between aggregated users' behaviour and the cryptocurrency pricing in exchange markets. This paper analyses the properties of the transaction network of Bitcoin. We consider four different representations of it, over a period of nine years since the Bitcoin creation and involving 16 million users and 283 million transactions. By analysing these networks, we show the existence of causal relationships between Bitcoin price movements and changes of its transaction network topology. Our results reveal the interplay between structural quantities, indicative of the collective behaviour of Bitcoin users, and price movements, showing that, during price drops, the system is characterised by a larger heterogeneity of nodes activity., Comment: 18 pages, 6 figures

The need to harmonise apparently irreconcilable arrangements in an ecosystem --nestedness and segregation-- has triggered so far different strategies. Methodological refinements, or the inclusion of behavioural preferences to the network dynamics offer a limited approach to the problem, since one remains constrained within a 2-dimensional view of an ecosystem, i.e. a presence-absence matrix. Here we question this partial-view paradigm, and show that nestedness and segregation may coexist across a varied range of scenarios. To do so, we rely on an upscaled representation of an ecological community as an $n$-partite hypergraph, inspired by Hutchinson's high-dimensional niche concept and the latest trends on ecological multilayer networks. This yields an inclusive description of an ecological system, for which we develop a natural extension of the definition of nestedness to larger dimensional spaces, revealing how competitive exclusion may operate regardless of a highly nested bipartite system., Comment: 11 pages, 4 figures

The functioning of the cryptocurrency Bitcoin relies on the open availability of the entire history of its transactions. This makes it a particularly interesting socio-economic system to analyse from the point of view of network science. Here we analyse the evolution of the network of Bitcoin transactions between users. We achieve this by using the complete transaction history from December 5th 2011 to December 23rd 2013. This period includes three bubbles experienced by the Bitcoin price. In particular, we focus on the global and local structural properties of the user network and their variation in relation to the different period of price surge and decline. By analysing the temporal variation of the heterogeneity of the connectivity patterns we gain insights on the different mechanisms that take place during bubbles, and find that hubs (i.e., the most connected nodes) had a fundamental role in triggering the burst of the second bubble. Finally, we examine the local topological structures of interactions between users, we discover that the relative frequency of triadic interactions experiences a strong change before, during and after a bubble, and suggest that the importance of the hubs grows during the bubble. These results provide further evidence that the behaviour of the hubs during bubbles significantly increases the systemic risk of the Bitcoin network, and discuss the implications on public policy interventions.

As new instances of nested organization --beyond ecological networks-- are discovered, scholars are debating around the co-existence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being solved, mainly for two reasons. First, nestedness and modularity appear to emerge from two contradictory dynamics, cooperation and competition. Second, existing methods to assess the presence of nestedness and modularity are flawed when it comes to the evaluation of concurrently nested and modular structures. In this work, we tackle the latter problem, presenting the concept of \textit{in-block nestedness}, a structural property determining to what extent a network is composed of blocks whose internal connectivity exhibits nestedness. We then put forward a set of optimization methods that allow us to identify such organization successfully, both in synthetic and in a large number of real networks. These findings challenge our understanding of the topology of ecological and social systems, calling for new models to explain how such patterns emerge., Comment: 16 pages, 5 figures, 1 Table

Hierarchical organization is an important, prevalent characteristic of complex systems; in order to understand their organization, the study of the underlying (generally complex) networks that describe the interactions between their constituents plays a central role. Numerous previous works have shown that many real-world networks in social, biologic and technical systems present hierarchical organization, often in the form of a hierarchy of community structures. Many artificial benchmark graphs have been proposed in order to test different community detection methods, but no benchmark has been developed to throughly test the detection of hierarchical community structures. In this study, we fill this vacancy by extending the Lancichinetti-Fortunato-Radicchi (LFR) ensemble of benchmark graphs, adopting the rule of constructing hierarchical networks proposed by Ravasz and Barab\'asi. We employ this benchmark to test three of the most popular community detection algorithms, and quantify their accuracy using the traditional Mutual Information and the recently introduced Hierarchical Mutual Information. The results indicate that the Ravasz-Barab\'asi-Lancichinetti-Fortunato-Radicchi (RB-LFR) benchmark generates a complex hierarchical structure constituting a challenging benchmark for the considered community detection methods., Comment: 9 pages, 9 figures

A comparative study across the most widely known blockchain technologies is conducted with a bottom-up approach. Blockchains are disentangled into building blocks. Each building block is then hierarchically classified in main and subcomponents. Then, alternative layouts for the subcomponents are identified and compared between them. Finally, a taxonomy tree summarises the study and provides a navigation tool across different blockchain architectural configurations., Comment: 43 pages, 1 figure

Established Open Source Software (OSS) projects can grow in size if new developers join, but also the number of OSS projects can grow if developers choose to found new projects. We discuss to what extent an established model for firm growth can be applied to the dynamics of OSS projects. Our analysis is based on a large-scale data set from SourceForge (SF) consisting of monthly data for 10 years, for up to 360'000 OSS projects and up to 340'000 developers. Over this time period, we find an exponential growth both in the number of projects and developers, with a remarkable increase of single-developer projects after 2009. We analyze the monthly entry and exit rates for both projects and developers, the growth rate of established projects and the monthly project size distribution. To derive a prediction for the latter, we use modeling assumptions of how newly entering developers choose to either found a new project or to join existing ones. Our model applies only to collaborative projects that are deemed to grow in size by attracting new developers. We verify, by a thorough statistical analysis, that the Yule-Simon distribution is a valid candidate for the size distribution of collaborative projects except for certain time periods where the modeling assumptions no longer hold. We detect and empirically test the reason for this limitation, i.e., the fact that an increasing number of established developers found additional new projects after 2009., Comment: 22 pages, 10 figures

The measurement of information flows within moving animal groups has recently been a topic of considerable interest, and it has become clear that the individual(s) that drive collective movement may change over time, and that such individuals may not necessarily always lead from the front. However, methods to quantify the influence of specific individuals on the behaviour of other group members and the direction of information flow in moving group, are lacking on the level of empirical studies and theoretical models. Using high spatio-temporal resolution GPS trajectories of foraging meerkats, Suricata suricatta, we provide an information-theoretic framework to identify dynamical coupling between animals independent of their relative spatial positions. Based on this identification, we then compare designations of individuals as either drivers or responders against designations provided by the relative spatial position. We find that not only does coupling occur both from the frontal to the trailing individuals and vice versa, but also that the coupling direction is a non-linear function of the relative position. This provides evidence for (i) intermittent fluctuation of the coupling strength and (ii) alternation in the coupling direction within foraging meerkat pairs. The framework we introduce allows for a detailed description of the dynamical patterns of mutual influence between all pairs of individuals within moving animal groups. We argue that applying an information-theoretic perspective to the study of coordinated phenomena in animal groups will eventually help to understand cause and effect in collective behaviour., Comment: 20 pages, 4 figures. Supplemental information: 16 pages, 9 figures. This manuscript was originally submitted to PNAS on June 5, 2013

How do humans respond to indirect social influence when making decisions? We analysed an experiment where subjects had to repeatedly guess the correct answer to factual questions, while having only aggregated information about the answers of others. While the response of humans to aggregated information is a widely observed phenomenon, it has not been investigated quantitatively, in a controlled setting. We found that the adjustment of individual guesses depends linearly on the distance to the mean of all guesses. This is a remarkable, and yet surprisingly simple, statistical regularity. It holds across all questions analysed, even though the correct answers differ in several orders of magnitude. Our finding supports the assumption that individual diversity does not affect the response to indirect social influence. It also complements previous results on the nonlinear response in information-rich scenarios. We argue that the nature of the response to social influence crucially changes with the level of information aggregation. This insight contributes to the empirical foundation of models for collective decisions under social influence., Comment: 3 figures

We study a system in which N agents have to decide between two strategies \theta_i (i \in 1... N), for defection or cooperation, when interacting with other n agents (either spatial neighbors or randomly chosen ones). After each round, they update their strategy responding nonlinearly to two different information sources: (i) the payoff a_i(\theta_i, f_i) received from the strategic interaction with their n counterparts, (ii) the fraction f_i of cooperators in this interaction. For the latter response, we assume social herding, i.e. agents adopt their strategy based on the frequencies of the different strategies in their neighborhood, without taking into account the consequences of this decision. We note that f_i already determines the payoff, so there is no additional information assumed. A parameter \zeta defines to what level agents take the two different information sources into account. For the strategic interaction, we assume a Prisoner's Dilemma game, i.e. one in which defection is the evolutionary stable strategy. However, if the additional dimension of social herding is taken into account, we find instead a stable outcome where cooperators are the majority. By means of agent-based computer simulations and analytical investigations, we evaluate the critical conditions for this transition towards cooperation. We find that, in addition to a high degree of social herding, there has to be a nonlinear response to the fraction of cooperators. We argue that the transition to cooperation in our model is based on less information, i.e. on agents which are not informed about the payoff matrix, and therefore rely on just observing the strategy of others, to adopt it. By designing the right mechanisms to respond to this information, the transition to cooperation can be remarkably enhanced., Comment: 22 pages, 7 figures

In this paper we focus on diversity-induced resonance, which was recently found in bistable, excitable and other physical systems. We study the appearance of this phenomenon in a purely economic model of cooperating and defecting agents. Agent's contribution to a public good is seen as a social norm. So defecting agents face a social pressure, which decreases if free-riding becomes widespread. In this model, diversity among agents naturally appears because of the different sensitivity towards the social norm. We study the evolution of cooperation as a response to the social norm (i) for the replicator dynamics, and (ii) for the logit dynamics by means of numerical simulations. Diversity-induced resonance is observed as a maximum in the response of agents to changes in the social norm as a function of the degree of heterogeneity in the population. We provide an analytical, mean-field approach for the logit dynamics and find very good agreement with the simulations. From a socio-economic perspective, our results show that, counter-intuitively, diversity in the individual sensitivity to social norms may result in a society that better follows such norms as a whole, even if part of the population is less prone to follow them., Comment: 19 pages, 6 figures

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold \theta_i determining their capacity to handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(\theta), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk., Comment: 23 pages, 7 Figures

We study correlations in temporal networks and introduce the notion of betweenness preference. It allows to quantify to what extent paths, existing in time-aggregated representations of temporal networks, are actually realizable based on the sequence of interactions. We show that betweenness preference is present in empirical temporal network data and that it influences the length of shortest time-respecting paths. Using four different data sets, we further argue that neglecting betweenness preference leads to wrong conclusions about dynamical processes on temporal networks., Comment: 10 pages, 4 figures

The structure of a society depends, to some extent, on the incentives of the individuals they are composed of. We study a stylized model of this interplay, that suggests that the more individuals aim at climbing the social hierarchy, the more society's hierarchy gets strong. Such a dependence is sharp, in the sense that a persistent hierarchical order emerges abruptly when the preference for social status gets larger than a threshold. This phase transition has its origin in the fact that the presence of a well defined hierarchy allows agents to climb it, thus reinforcing it, whereas in a "disordered" society it is harder for agents to find out whom they should connect to in order to become more central. Interestingly, a social order emerges when agents strive harder to climb society and it results in a state of reduced social mobility, as a consequence of ergodicity breaking, where climbing is more difficult., Comment: 14 pages, 9 figures