Dynamical partitions of space in any dimension

Topologically stable cellular partitions of D dimensional spaces are studied. A complete statistical description of the average structural properties of such partition is given in term of a sequence of D/2-1 (or (D-1)/2) variables for D even (or odd). These variables are the average coordination numbers of the 2k-dimensional polytopes (2k < D) which make the cellular structure. A procedure to built D dimensional space partitions trough cell-division and cell-coalescence transformations is presented. Classes of structures which are invariant under these transformations are found and the average properties of such structures are illustrated. Homogeneous partitions are constructed and compared with the known structures obtained by Voronoi partitions and sphere packings in high dimensions.Comment: LaTeX 5 eps figures, submetted to J. Phys.

A Decentralised Digital Identity Architecture

Current architectures to validate, certify, and manage identity are based on centralised, top-down approaches that rely on trusted authorities and third-party operators. We approach the problem of digital identity starting from a human rights perspective, with a primary focus on identity systems in the developed world. We assert that individual persons must be allowed to manage their personal information in a multitude of different ways in different contexts and that to do so, each individual must be able to create multiple unrelated identities. Therefore, we first define a set of fundamental constraints that digital identity systems must satisfy to preserve and promote privacy as required for individual autonomy. With these constraints in mind, we then propose a decentralised, standards-based approach, using a combination of distributed ledger technology and thoughtful regulation, to facilitate many-to-many relationships among providers of key services. Our proposal for digital identity differs from others in its approach to trust in that we do not seek to bind credentials to each other or to a mutually trusted authority to achieve strong non-transferability. Because the system does not implicitly encourage its users to maintain a single aggregated identity that can potentially be constrained or reconstructed against their interests, individuals and organisations are free to embrace the system and share in its benefits.Comment: 30 pages, 10 figures, 3 table

The cost of Bitcoin mining has never really increased

The Bitcoin network is burning a large amount of energy for mining. In this paper we estimate the lower bound for the global energy cost for a period of ten years from 2010, taking into account changing oil costs, improvements in hashing technologies and hashing activity. Despite a ten-billion-fold increase in hashing activity and a ten-million-fold increase in total energy consumption, we find the cost relative to the volume of transactions has not increased nor decreased since 2010. This is consistent with the perspective that, in order to keep a the Blockchain system secure from double spending attacks, the proof or work must cost a sizable fraction of the value that can be transferred through the network. We estimate that in the Bitcoin network this fraction is of the order of 1%.Comment: 16 pages, 6 figure

Cryptocurrency market structure: connecting emotions and economics

We study the dependency and causality structure of the cryptocurrency market investigating collective movements of both prices and social sentiment related to almost two thousand cryptocurrencies traded during the first six months of 2018. This is the first study of the whole cryptocurrency market structure. It introduces several rigorous innovative methodologies applicable to this and to several other complex systems where a large number of variables interact in a non-linear way, which is a distinctive feature of the digital economy. The analysis of the dependency structure reveals that prices are significantly correlated with sentiment. The major, most capitalised cryptocurrencies, such as bitcoin, have a central role in the price correlation network but only a marginal role in the sentiment network and in the network describing the interactions between the two. The study of the causality structure reveals a causality network that is consistently related with the correlation structures and shows that both prices cause sentiment and sentiment cause prices across currencies with the latter being stronger in size but smaller in number of significative interactions. Overall our study uncovers a complex and rich structure of interrelations where prices and sentiment influence each other both instantaneously and with lead-lag causal relations. A major finding is that minor currencies, with small capitalisation, play a crucial role in shaping the overall dependency and causality structure. Despite the high level of noise and the short time-series we verified that these networks are significant with all links statistically validated and with a structural organisation consistently reproduced across all networks.Comment: 17 pages, 5 figures, 2 table