Connecting complex networks to nonadditive entropies.

Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space-time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its 'energy' distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann-Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the [Formula: see text] limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

Data-driven study of the COVID-19 pandemic via age-structured modelling and prediction of the health system failure in Brazil amid diverse intervention strategies.

In this work we propose a data-driven age-structured census-based SIRD-like epidemiological model capable of forecasting the spread of COVID-19 in Brazil. We model the current scenario of closed schools and universities, social distancing of people above sixty years old and voluntary home quarantine to show that it is still not enough to protect the health system by explicitly computing the demand for hospital intensive care units. We also show that an urgent intense quarantine might be the only solution to avoid the collapse of the health system and, consequently, to minimize the quantity of deaths. On the other hand, we demonstrate that the relaxation of the already imposed control measures in the next days would be catastrophic.

Statistical Properties of the Quantum Internet.

Steady technological advances are paving the way for the implementation of the quantum internet, a network of locations interconnected by quantum channels. Here we propose a model to simulate a quantum internet based on optical fibers and employ network-theory techniques to characterize the statistical properties of the photonic networks it generates. Our model predicts a continuous phase transition between a disconnected and a highly connected phase and that the typical photonic networks do not present the small world property. We compute the critical exponents characterizing the phase transition, provide quantitative estimates for the minimum density of nodes needed to have a fully connected network and for the average distance between nodes. Our results thus provide quantitative benchmarks for the development of a quantum internet.

Machine Learning Nonlocal Correlations.

The ability to witness nonlocal correlations lies at the core of foundational aspects of quantum mechanics and its application in the processing of information. Commonly, this is achieved via the violation of Bell inequalities. Unfortunately, however, their systematic derivation quickly becomes unfeasible as the scenario of interest grows in complexity. To cope with that, here, we propose a machine learning approach for the detection and quantification of nonlocality. It consists of an ensemble of multilayer perceptrons blended with genetic algorithms achieving a high performance in a number of relevant Bell scenarios. As we show, not only can the machine learn to quantify nonlocality, but discover new kinds of nonlocal correlations inaccessible with other current methods as well. We also apply our framework to distinguish between classical, quantum, and even postquantum correlations. Our results offer a novel method and a proof-of-principle for the relevance of machine learning for understanding nonlocality.

Scaling properties of d-dimensional complex networks.

The area of networks is very interdisciplinary and exhibits many applications in several fields of science. Nevertheless, there are few studies focusing on geographically located d-dimensional networks. In this paper, we study the scaling properties of a wide class of d-dimensional geographically located networks which grow with preferential attachment involving Euclidean distances through r_{ij}^{-α_{A}} (α_{A}≥0). We have numerically analyzed the time evolution of the connectivity of sites, the average shortest path, the degree distribution entropy, and the average clustering coefficient for d=1,2,3,4 and typical values of α_{A}. Remarkably enough, virtually all the curves can be made to collapse as functions of the scaled variable α_{A}/d. These observations confirm the exist- ence of three regimes. The first one occurs in the interval α_{A}/d∈[0,1]; it is non-Boltzmannian with very-long-range interactions in the sense that the degree distribution is a q exponential with q constant and above unity. The critical value α_{A}/d=1 that emerges in many of these properties is replaced by α_{A}/d=1/2 for the ß exponent which characterizes the time evolution of the connectivity of sites. The second regime is still non-Boltzmannian, now with moderately-long-range interactions, and reflects in an index q monotonically decreasing with α_{A}/d increasing from its critical value to a characteristic value α_{A}/d≃5. Finally, the third regime is Boltzmannian-like (with q≃1) and corresponds to short-range interactions.

Role of dimensionality in complex networks.

Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form , where the q-exponential form optimizes the nonadditive entropy Sq (which, for q → 1, recovers the Boltzmann-Gibbs entropy). We introduce and study here d-dimensional geographically-located networks which grow with preferential attachment involving Euclidean distances through . Revealing the connection with q-statistics, we numerically verify (for d = 1, 2, 3 and 4) that the q-exponential degree distributions exhibit, for both q and k, universal dependences on the ratio αA/d. Moreover, the q = 1 limit is rapidly achieved by increasing αA/d to infinity.