arXiv subjects

P. Ribeca

Publications and source records attributed to P. Ribeca.

3 recordsLinked to original sources

arXiv2021

Networks of Ethereum Non-Fungible Tokens: A graph-based analysis of the ERC-721 ecosystem

Non-fungible tokens (NFTs) as a decentralized proof of ownership represent one of the main reasons why Ethereum is a disruptive technology. This paper presents the first systematic study of the interactions occurring in a number of NFT ecosystems. We illustrate how to retrieve transaction data available on the blockchain and structure it as a graph-based model. Thanks to this methodology, we are able to study for the first time the topological structure of NFT networks and show that their properties (degree distribution and others) are similar to those of interaction graphs in social networks. Time-dependent analysis metrics, useful to characterize market influencers and interactions between different wallets, are also introduced. Based on those, we identify across a number of NFT networks the widespread presence of both investors accumulating NFTs and individuals who make large profits.

cs.SI↗

arXiv2007

From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions

This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has hitherto not received the attention it actually deserves. The unifying concept for convergence acceleration methods is that in many cases, one can reach much faster convergence than by adding a particular series term by term. In some cases, it is even possible to use a divergent input series, together with a suitable sequence transformation, for the construction of numerical methods that can be applied to the calculation of special functions. This review both aims to provide some practical guidance as well as a groundwork for the study of specialized literature. As a second topic, we review some recent developments in the field of Borel resummation, which is generally recognized as one of the most versatile methods for the summation of factorially divergent (perturbation) series. Here, the focus is on algorithms which make optimal use of all information contained in a finite set of perturbative coefficients. The unifying concept for the various aspects of the Borel method investigated here is given by the singularities of the Borel transform, which introduce ambiguities from a mathematical point of view and lead to different possible physical interpretations. The two most important cases are: (i) the residues at the singularities correspond to the decay width of a resonance, and (ii) the presence of the singularities indicates the existence of nonperturbative contributions which cannot be accounted for on the basis of a Borel resummation and require generalizations toward resurgent expansions. Both of these cases are illustrated by examples.

physics.comp-ph↗

arXiv2005

The Topology of Pseudoknotted Homopolymers

We consider the folding of a self-avoiding homopolymer on a lattice, with saturating hydrogen bond interactions. Our goal is to numerically evaluate the statistical distribution of the topological genus of pseudoknotted configurations. The genus has been recently proposed for classifying pseudoknots (and their topological complexity) in the context of RNA folding. We compare our results on the distribution of the genus of pseudoknots, with the theoretical predictions of an existing combinatorial model for an infinitely flexible and stretchable homopolymer. We thus obtain that steric and geometric constraints considerably limit the topological complexity of pseudoknotted configurations, as it occurs for instance in real RNA molecules. We also analyze the scaling properties at large homopolymer length, and the genus distributions above and below the critical temperature between the swollen phase and the compact-globule phase, both in two and three dimensions.

q-bio.BM↗