A journey through mapping space: characterising the statistical and metric properties of reduced representations of macromolecules

A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the mapping space has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang–Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space, which mark the boundaries between qualitatively different reduced representations of the same molecule. Graphicabstract

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence $$q_c$$ q c in case of conformity is independent from the size of the source of influence $$q_a$$ q a in case of anticonformity. For $$q_c=q_a=q$$ q c = q a = q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for $$q_c \ge q_a + \Delta q$$ q c ≥ q a + Δ q , where $$\Delta q=4$$ Δ q = 4 for $$q_a \le 3$$ q a ≤ 3 and $$\Delta q=3$$ Δ q = 3 for $$q_a>3$$ q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree $$\langle k\rangle \le 150$$ ⟨ k ⟩ ≤ 150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of $$\langle k\rangle$$ ⟨ k ⟩ . Moreover, we show that for $$q_a < q_c - 1$$ q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for $$q_a \ge q_c - 1$$ q a ≥ q c - 1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to $$\langle k\rangle$$ ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition.

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability $$1-p$$ 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $$s>2$$ s > 2 the model displays discontinuous phase transitions for any $$q>1$$ q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $$q>5$$ q > 5 . Moreover, unlike the case of $$s=2$$ s = 2 , for $$s>2$$ s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

Influencer identification in dynamical complex systems

The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different perspectives, and present state-of-the-art solutions designed for different objectives. In particular, we first discuss the problem of finding the minimal number of nodes whose removal would breakdown the network (i.e. the optimal percolation or network dismantle problem), and then survey methods to locate the essential nodes that are capable of shaping global dynamics with either continuous (e.g. independent cascading models) or discontinuous phase transitions (e.g. threshold models). We conclude the review with a summary and an outlook.