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Forks of Bitcoin. Schematic representation of Bitcoin forking tree. Each time a new cryptocurrency is created, its code (software fork) or its blockchain (hard fork) can be used as a starting point for the creation of new coins and blockchains. For instance Litecoin has been created by minor modifications of Bitcoin code and in its turn Litecoin source code has been used to develop many other coins such as the well known Dogecoin. The creation of new cryptocurrencies can be described in terms of an adjacent possible process. Figure created with www.diagrams.net.
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Blockchains are among the most relevant emerging technologies of recent times and, according to many, they will have a central role in shaping the future of our society. Since the introduction of Bitcoin in 2009, the first notorious blockchain system bound to a cryptocurrency, the blockchain ecosystem has experienced a huge growth, driven by innova...
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Citations
... For instance, if we have a book in mind, then t would be the number of words composing it, while D would correspond to the number of different words it contains. Heaps' law is observed in several systems ranging from language and cities to cryptocurrencies, and Wikipedia pages [11,[14][15][16], and it is strictly connected with the presence of underlying power-law distributions [14,17]. ...
... After its introduction, the UMT has been used to model, among others, innovation in the cryptocurrency market [16], interacting discovery processes [18], and the emergence and evolution of social networks [19]. However, despite its versatility, the UMT cannot, in its simplest form, reproduce innovation processes described by functional forms different from the Heaps' law Eq. ...
Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The urn model with triggering (UMT) has been instrumental in modeling these innovation dynamics. Yet a generalization is needed to capture the richer empirical phenomenology. Here we introduce a time-dependent urn model with triggering (TUMT), a generalization of the UMT that crucially integrates time-dependent parameters for reinforcement and triggering to offer a broader framework for modeling innovation in nonstationary systems. Through analytical computation and numerical simulations, we show that the TUMT reconciles various behaviors observed in a broad spectrum of systems from patenting activity to the analysis of gene mutations. We highlight how the TUMT features a “critical” region where both Heaps' and Zipf's laws coexist, for which we compute the exponents.
Published by the American Physical Society 2025
... Building upon the work of Pólya 33,34 , the UMT adds to the traditional reinforcement mechanism of the Pólya urn's scheme a triggering mechanism that expands the space of possible discoveries upon the extraction of each novelty. Being able to reproduce the empirical laws and thanks to its simplicity, the UMT has been used to study various systems with an expanding set of "items", like the rise and fall of popularity in technological and artistic productions 2 , the emergence and evolution of social networks 35 , and the evolution of the cryptocurrency ecosystem 36 . One could also picture ideas, concepts, or items as the linked elements of an abstract network. ...
Studying how we explore the world in search of novelties is key to understand the mechanisms that can lead to new discoveries. Previous studies analyzed novelties in various exploration processes, defining them as the first appearance of an element. However, novelties can also be generated by combining what is already known. We hence define higher-order novelties as the first time two or more elements appear together, and we introduce higher-order Heaps’ exponents as a way to characterize their pace of discovery. Through extensive analysis of real-world data, we find that processes with the same pace of discovery, as measured by the standard Heaps’ exponent, can instead differ at higher orders. We then propose to model an exploration process as a random walk on a network in which the possible connections between elements evolve in time. The model reproduces the empirical properties of higher-order novelties, revealing how the network we explore changes over time along with the exploration process.
... There are numerous types of cryptocurrencies, with stablecoins maintaining value by pegging to fiat currencies or commodities. Bitcoin has advantages in terms of security, brand recognition, and a large user base, allowing it to both compete with other cryptocurrencies and support the development of its ecosystem [8,9]. ...
Amidst uncertainties of the global economy and new ideals up in the air, new forms of currencies have emerged as a result of globalization. While fiat currency still prevails on the international stage, cryptocurrency has taken advantage to become a vital part of economies. The fact that each of these currencies has its own characteristics, strengths and weaknesses, and is not proportional to economic development has led to a wider debate on the relative benefits of each currency for developing countries. In particular, whether cryptocurrencies can help improve the economic situation in developing countries with their unique advantages. Even though there are limited case studies since cryptocurrency requires some barrier for adoption, theoretical arguments make it sound appealing. Through case studies of El Salvador, Central African Republics, and India with regard to tangible changes brought by cryptocurrency and policy changes, this paper explores how well the theoretical benefits have been implemented in practice. While many intricate factors are reacting to each other with such changes, making the results harder to evaluate with linear measurements, inherent shortcomings in implementations seem to be hindering the benefits of cryptocurrency. Therefore, the results show that the use of cryptocurrency as a legal tender may not lead to an improvement in the economic system and conditions in developing countries due to its high barrier to entry. In order to maximize the benefits of cryptocurrencies, there is a need to improve infrastructure to make cryptocurrencies more accessible.
... It is well known that discovery processes are typically described by Heaps' law, which relates the number of distinct elements D(t) experienced to the total number of elements t by a sublinear scaling D(t) ∼ t β . This law has been observed in numerous systems [4,[22][23][24][25][26], including online platforms [7]. It is thus natural to question if it is affected by the presence of recommendation algorithms and how they may alter the scaling exponent β. ...
Recommender systems are vital for shaping user online experiences. While some believe they may limit new content exploration and promote opinion polarization, a systematic analysis is still lacking. In this paper we present a model that explores the influence of recommender systems on novel content discovery. Surprisingly, analytical and numerical findings reveal that these techniques can enhance novelty discovery rates. Also, distinct algorithms with similar discovery rates yield different outcomes, with the matrix factorization algorithm producing opinion polarization. Our approach shed light on the interplay between algorithmic recommendations and novelties discovery, offering a framework to enhance recommendation techniques beyond accuracy metrics.
... Cryptocurrencies, often referred to as digital or virtual currencies, have redefined the way we think about money, transactions, and financial systems. Born from the ambition of creating decentralised and secure systems for digital transactions, they have rapidly evolved into a dynamic and diverse ecosystem powered by the blockchain (Marzo et al., 2022). While Bitcoin initiated the crypto revolution, thousands of alterna-tive cryptocurrencies have also emerged, each with its unique features and applications (CoinMarketCap, 2023). ...
This chapter presents a systematic literature review on consumer adoption
of cryptocurrencies as a function of three key constructs: consumer gender, personality traits, and overconfidence aspects. After having introduced the topic of cryptocurrencies, we structure our review across these three fundamental building blocks by briefly describing the existing state of the art regarding demographic and psychographic predictors of consumers’ crypto-related decisions. We summarize the main
findings in this domain, while also illustrating through which empirical evidence such results have emerged in terms of, for example, representativeness, sample sizes, and sample nationalities. Finally, we conclude by noting areas of improvement in the existing literature and stating a series of fruitful avenues for future research.
... The Blockchain [35,36] technology and cryptocurrencies, such as Bitcoin (BTC), Ethereum, and many others [37], are pervading various aspects of our society. Cryptocurrencies are the main application of the Blockchain [38]. ...
Taking informed decisions, namely acting rationally, is an individual attitude of paramount relevance in nature and human societies.
In this work, we study how rationality spreads in a community.
To this end, through an agent-based model, we analyse the dynamics of a population whose individuals, endowed with a rational attitude controlled by a numerical parameter, play a simple game. The latter consists of multiple strategies, each associated with a given reward.
The proposed model is then used as a benchmark for studying the behaviour of Bitcoin users, inferred by analysing transactions recorded in the Blockchain.
Remarkably, a population undergoing a sharp transition from irrational to rational attitudes shows a behavioural pattern similar to that of Bitcoin users, whose rationality showed up as soon as their cryptocurrency became worth just a few cents (USD).
To conclude, a behavioural analysis that relies on an entropy measure combined with a simple agent-based model allows us to detect the rise of rationality across a community.
Although further investigations are essential to corroborate our results, we deem the proposed approach could also get used for studying other social phenomena and behaviours.
... While these developments offer great opportunities, fundamental questions arise regarding the dynamics of Bitcoin (BTC) dominance in the cryptocurrency ecosystem (Marzo et al., 2022). How do changes in Bitcoin's dominance phase affect AltCoin price movements, especially Ethereum (ETH)? ...
... Decentralization is a key concept in the development of cryptocurrencies, and this is realized through the use of blockchain technology. Blockchain is a form of distribution technology that allows transaction records to be recorded in a decentralized and encrypted manner (Chu et al., 2024;Marzo et al., 2022;Routledge & Zetlin-Jones, 2022). This uniqueness has a positive impact on the security and sustainability of cryptocurrencies (Ghosh et al., 2020). ...
The main objective of this research is to optimize the understanding of AltCoin price synchronization, with a focus on Ethereum, during different periods of Bitcoin dominance. This research uses secondary data through 162 observations for each cryptocurrency collected (BTC and ETH). The Vector Autoregressive (VAR)/Vector Error Correction Model (VECM) method is used as the analytical technique. The findings of this study have the potential to provide a strong foundation for the development of investment strategies in the cryptocurrency market. This study has identified different impact patterns on AltCoin prices during the High, Middle and Low Dominance Phases. The research findings reflect different impact patterns depending on the phase of Bitcoin dominance, indicating the complexity of market dynamics related to certain factors.
... These tokens are also called cryptocurrencies, or cryptos, due to the underlying cryptographic mechanisms supporting and securing transactions. Nowadays, a crypto ecosystem [4][5][6][7] which includes, for instance, Ethereum (ETH), XRP (XRP), Cardano (ADA), Bitcoin Cash (BCH), Solana (SOL), Dogecoin (DOGE), Bitcoin Satoshi Vision (BSV), and many other tokens, continuously grows. Many cryptos of such an ecosystem get exchanged in the crypto market, today accessible by several trading platforms. ...
The structure and the number of bitcoin transactions encoded in the Blockchain reflect the behaviour of Bitcoin owners.
Likewise, the formation of bullish and bearish trends in the crypto market reflects the behaviour of Bitcoin traders.
Inspired by the above observations, in this work, we aim to assess whether human behaviour underlies some relationships between the Blockchain and the crypto market.
To this end, we map the Blockchain to a spin-lattice whose configurations, representing the behaviour of Bitcoin owners, form ordered and disordered patterns.
This 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, in addition, to find that disordered patterns in the Blockchain precede Bitcoin panic selling.
Results suggest that human behaviour, underlying Blockchain evolution and the crypto market, brings a fascinating connection between disorder and panic in Bitcoin dynamics to light.
... Additionally, Podder (2023) and Coulter (2022) explain that cryptocurrencies are often highly volatile, which can produce sharp price fluctuations in a short period, regardless of limited supply or possible inflation. Therefore, it is important to understand the specific characteristics of each particular Cryptocurrency when considering its impact on inflation and deflation in the cryptocurrency economy (Cahyadi et al., 2021;Marzo et al., 2022). ...
This research aims to determine the impact of Cryptocurrency on macroeconomics, especially in terms of inflation, exchange rates, and other relevant aspects. This article also analyzes the various regulatory approaches that governments around the world have implemented to address risks and manage the development of cryptocurrencies. The method used in this research is qualitative with a descriptive-analytic approach. The methods used in this research include collecting data from various sources, including historical cryptocurrency data, macroeconomic data, and cryptocurrency regulatory data. The results of the analysis show that cryptocurrencies can have a significant impact on macroeconomic stability, both positive and negative, depending on factors such as widespread use, price volatility, and role in the global financial system. Additionally, the different regulatory approaches reflect the diversity of global views on cryptocurrencies and the challenges of regulating technological innovation. This article summarizes these findings and underscores the importance of a deep understanding of cryptocurrencies in the era of digital finance.
... Bitcoin is arguably the very first wide-spread application of blockchain technology (Nakamoto 2008). In terms of transaction usage, trade volume, mar-ket capitalization, and the overall attention it receives, bitcoin has remained the dominant cryptocurrency (Koutmos and Wei 2023;Marzo et al. 2022). ...
This article explores the extent to which network activity can explain changes in Ethereum transaction fees. Such fees are referred to as “gas prices” within the Ethereum blockchain, and are important inputs not only for executing transactions, but also for the deployment of smart contracts within the network. Using a bootstrapped quantile regression model, it can be shown that network activity, such as the sizes of blocks or the number of transactions and contracts, can have a heterogeneous relationship with gas prices across periods of low and high gas price changes. Of all the network activity variables examined herein, the number of intraday transactions within Ethereum’s blockchain is most consistent in explaining gas fees across the full distribution of gas fee changes. From a statistical perspective, the bootstrapped quantile regression approach demonstrates that linear modeling techniques may yield but a partial view of the rich dynamics found in the full range of gas price changes’ conditional distribution. This is an important finding given that Ethereum’s blockchain has undergone fundamental economic and technological regime changes, such as the recent implementation of the Ethereum Improvement Proposal (EIP) 1559, which aims to provide an algorithmic updating rule to estimate Ethereum’s “base fee”.
