Advances in Complex Systems

Smart contract risk can be defined as a financial risk of loss due to cyber attacks on or contagious failures of smart contracts. Its quantification is of paramount importance to technology platform providers as well as companies and individuals when considering the deployment of this new technology. That is why, as our primary contribution, we propose a structural framework of aggregate loss distribution for smart contract risk under the assumption of a tree-stars graph topology representing the network of interactions among smart contracts and their users. To our knowledge, there exist no theoretical frameworks or models of an aggregate loss distribution for smart contracts in this setting. To achieve our goal, we contextualize the problem in the probabilistic graph-theoretical framework using bond percolation models. We assume that the smart contract network topology is represented by a random tree graph of finite size, and that each smart contract is the center of a random star graph whose leaves represent the users of the smart contract. We allow for heterogeneous loss topology superimposed on this smart contract and user topology and provide analytical results and instructive numerical examples.

The principle of least effort (PLE) is believed to be a universal rule for living systems. Its application to the derivation of the power law probability distributions of living systems has long been challenging. Recently, a measure of efficiency was proposed as a tool of deriving Zipf’s and Pareto’s laws directly from the PLE. This work is a further investigation of this efficiency measure from a mathematical point of view. The aim is to get further insight into its properties and usefulness as a metric of performance. We address some key mathematical properties of this efficiency such as its sign, uniqueness and robustness. We also look at the relationship between this measure and other properties of the system of interest such as inequality and uncertainty, by introducing a new method for calculating nonnegative continuous entropy.

Since the subprime mortgage crisis, it is urgent to quantify the systemic financial risk and the network externality from the vulnerable perspective. Based on the overlapping portfolio, this study constructs an optimal leverage decision-making model with deleveraging and the fire sales mechanism to describe the liquidity risk spillover effects. Through the empirical results, the institution of a larger size should be more systematically important. Higher leverages account for more vulnerability, while institutions with higher interest ratios of revenue or cost and capital adequacy ratios would be more invulnerable.

Twitter is a popular social medium for sharing opinions and engaging in topical debates, yet presents a wide spread of misinformation, especially in political debates, from bots and adversarial attacks. The current state-of-the-art methods for detecting humans and bots in Twitter often lack generalizability beyond English. Here, a language-agnostic method to detect real users and their interactions by leveraging network topology from retweets is presented. To that end, the chosen topic is COVID-19 policies in Mexico, which has been considered by users as polemic. Two kinds of network are built: a directed network of retweets; and the co-event network, where a non-directed link between two users exists if they have retweeted the same post in a given time window (projection of a bipartite network). Then, single node properties of these networks, such as the clustering coefficient and the degree, are studied. Three kinds of users are observed: some with a high clustering coefficient but a very small degree, a second group with zero clustering coefficient and a variable degree, and a third group in which the clustering coefficient as a function of the degree decays as a power law. This third group represents ∼2% of the users and is characteristic of dynamical networks with feedback. The latter seems to represent strongly interacting followers/followed in a real social network as confirmed by an inspection of such nodes. A percolation analysis of the resulting co-retweet and co-hashtag network reveals the relevance of such weak links, typical of real social human networks. The presented methods are simple to implement in other social media platforms and can be used to mitigate misinformation and conflicts.