We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations reveals a higher correlation compared to the shortest-path approach used previously. In addition our method allows to connect fundamental observables in epidemic spreading with the cumulant-generating function of the hitting time for a Markov chain. Our results provides a general and computationally efficient approach using only algebraic methods.

A pivotal idea in network science, marketing research and innovation diffusion theories is that a small group of nodes -called influencers -have the largest impact on social contagion and epidemic processes in networks. Despite the long-standing interest in the influencers identification problem in socio-economic and biological networks, there is not yet agreement on which is the best identification strategy. State-of-the-art strategies are typically based either on heuristic centrality measures or on analytic arguments that only hold for specific network topologies or peculiar dynamical regimes. Here, we leverage the recently introduced random-walk effective distance -a topological metric that estimates almost perfectly the arrival time of diffusive spreading processes on networks -to introduce a new centrality metric which quantifies how close a node is to the other nodes. We show that the new centrality metric significantly outperforms state-of-the-art metrics in detecting the influencers for global contagion processes. Our findings reveal the essential role of the network effective distance for the influencers identification and lead us closer to the optimal solution of the problem.

The recent epidemic of Coronavirus (COVID-19) that started in China has already been "exported" to more than 140 countries in all the continents, evolving in most of them by local spreading. In this contribution we analyze the trends of the cases reported in all the Chinese provinces, as well as in some countries that, until March 15th, 2020, have more than 500 cases reported. Notably and differently from other epidemics, the provinces did not show an exponential phase. The data available at the Johns Hopkins University site seem to fit well an algebraic sub-exponential growing behavior as was pointed out recently. All the provinces show a clear and consistent pattern of slowing down with growing exponent going nearly zero, so it can be said that the epidemic was contained in China. On the other side, the more recent spread in countries like, Italy, Iran, and Spain show a clear exponential growth, as well as other European countries. Even more recently, US -which was one of the first countries to have an individual infected outside China (Jan 21st, 2020)- seems to follow the same path. We calculate the exponential growth of the most affected countries, showing the evolution along time after the first local case. We identify clearly different patterns in the analyzed data and we give interpretations and possible explanations for them. The analysis and conclusions of our study can help countries that, after importing some cases, are not yet in the local spreading phase, or have just started

The effect of quenched sequence disorder on the thermodynamics of RNA secondary structure formation is investigated for two- and four-letter alphabet models using the constrained annealing approach, from which the temperature behavior of the free energy, specific heat, and helicity is analytically obtained. For competing base pairing energies, the calculations reveal reentrant melting at low temperatures, in excellent agreement with numerical results. Our results suggest an additional mechanism for the experimental phenomenon of RNA cold denaturation.

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