The COVID-19 pandemic forced countries all over the world to take unprecedented measures, like nationwide lockdowns. To adequately understand the emotional and social repercussions, a large-scale reconstruction of how people perceived these unexpected events is necessary but currently missing. We address this gap through social media by introducing MERCURIAL (Multi-layer Co-occurrence Networks for Emotional Profiling), a framework which exploits linguistic networks of words and hashtags to reconstruct social discourse describing real-world events. We use MERCURIAL to analyse 101,767 tweets from Italy, the first country to react to the COVID-19 threat with a nationwide lockdown. The data were collected between the 11th and 17th March, immediately after the announcement of the Italian lockdown and the WHO declaring COVID-19 a pandemic. Our analysis provides unique insights into the psychological burden of this crisis, focussing on—(i) the Italian official campaign for self-quarantine (#iorestoacasa), (ii) national lockdown (#italylockdown), and (iii) social denounce (#sciacalli). Our exploration unveils the emergence of complex emotional profiles, where anger and fear (towards political debates and socio-economic repercussions) coexisted with trust, solidarity, and hope (related to the institutions and local communities). We discuss our findings in relation to mental well-being issues and coping mechanisms, like instigation to violence, grieving, and solidarity. We argue that our framework represents an innovative thermometer of emotional status, a powerful tool for policy makers to quickly gauge feelings in massive audiences and devise appropriate responses based on cognitive data.

In this paper, we investigate influence maximization, or optimal opinion control, in a modified version of the two-state voter dynamics in which a native state and a controlled or influenced state are accounted for. We include agent predispositions to resist influence in the form of a probability q with which agents spontaneously switch back to the native state when in the controlled state. We argue that in contrast to the original voter model, optimal control in this setting depends on q: For low strength of predispositions q, optimal control should focus on hub nodes, but for large q, optimal control can be achieved by focusing on the lowest degree nodes. We investigate this transition between hub and low-degree node control for heterogeneous undirected networks and give analytical and numerical arguments for the existence of two control regimes.

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.

In this paper we analyze influence maximization in the voter model with an active strategic and a passive influencing party in non-stationary settings. We thus explore the dependence of optimal influence allocation on the time horizons of the strategic influencer. We find that on undirected heterogeneous networks, for short time horizons, influence is maximized when targeting low-degree nodes, while for long time horizons influence maximization is achieved when controlling hub nodes. Furthermore, we show that for short and intermediate time scales influence maximization can exploit knowledge of (transient) opinion configurations. More in detail, we find two rules. First, nodes with states differing from the strategic influencer's goal should be targeted. Second, if only few nodes are initially aligned with the strategic influencer, nodes subject to opposing influence should be avoided, but when many nodes are aligned, an optimal influencer should shadow opposing influence.

In this paper we analyze the effects of mistakes in opinion propagation in the voter model on strategic influence maximization. We provide numerical results and analytical arguments to show that generally two regimes exist for optimal opinion control: a regime of low transmission errors in which influence maximizers should focus on hub nodes and a large-error regime in which influence maximizers should focus on low-degree nodes. We also develop a degree-based mean-field theory and apply it to random networks with bimodal degree distribution, finding that analytical results for the dependence of regimes on parameters qualitatively agree with numerical results for scale-free networks. We generally find that the regime of optimal hub control is the larger, the more heterogeneous the social network and the smaller the more resources both available to the influencers.