#articles Generalized entropies, density of states, and non-extensivity
Sámuel G. Balogh, Gergely Palla, Péter Pollner & Dániel Czégel
Scientific Reports volume 10, Article number: 15516 (2020)
Abstract
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the number of variables, making the Boltzmann–Gibbs–Shannon entropy extensive. In systems with strongly interacting variables, or with variables driven by history-dependent dynamics, this is no longer true. Here we show that contrary to the generally held belief, not only strong correlations or history-dependence, but skewed-enough distribution of visiting probabilities, that is, first-order statistics, also play a role in determining the relation between configuration space size and system size, or, equivalently, the extensive form of generalized entropy. We present a macroscopic formalism describing this interplay between first-order statistics, higher-order statistics, and configuration space growth. We demonstrate that knowing any two strongly restricts the possibilities of the third. We believe that this unified macroscopic picture of emergent degrees of freedom constraining mechanisms provides a step towards finding order in the zoo of strongly interacting complex systems.
Sámuel G. Balogh, Gergely Palla, Péter Pollner & Dániel Czégel
Scientific Reports volume 10, Article number: 15516 (2020)
Abstract
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the number of variables, making the Boltzmann–Gibbs–Shannon entropy extensive. In systems with strongly interacting variables, or with variables driven by history-dependent dynamics, this is no longer true. Here we show that contrary to the generally held belief, not only strong correlations or history-dependence, but skewed-enough distribution of visiting probabilities, that is, first-order statistics, also play a role in determining the relation between configuration space size and system size, or, equivalently, the extensive form of generalized entropy. We present a macroscopic formalism describing this interplay between first-order statistics, higher-order statistics, and configuration space growth. We demonstrate that knowing any two strongly restricts the possibilities of the third. We believe that this unified macroscopic picture of emergent degrees of freedom constraining mechanisms provides a step towards finding order in the zoo of strongly interacting complex systems.
Nature
Generalized entropies, density of states, and non-extensivity
Scientific Reports - Generalized entropies, density of states, and non-extensivity
#articles Pseudo-Darwinian evolution of physical flows in complex networks
Geoffroy Berthelot, Liubov Tupikina, Min-Yeong Kang, Bernard Sapoval & Denis S. Grebenkov
Scientific Reports volume 10, Article number: 15477 (2020)
Abstract
The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and “Pseudo-Darwinian” strategy. At each evolution step and regarding the selected strategy, one removes either a randomly chosen link, or the link carrying the strongest flux, or the link with the weakest flux, respectively. We study how the network structure and the total flux between randomly chosen source and drain nodes evolve. We discover a universal power-law decrease of the total flux, followed by an abrupt transport collapse. The time of collapse is shown to be determined by the average number of links per node in the initial network, highlighting the importance of this network property for ensuring safe and robust transport against random failures, intentional attacks and maintenance cost optimizations.
Geoffroy Berthelot, Liubov Tupikina, Min-Yeong Kang, Bernard Sapoval & Denis S. Grebenkov
Scientific Reports volume 10, Article number: 15477 (2020)
Abstract
The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and “Pseudo-Darwinian” strategy. At each evolution step and regarding the selected strategy, one removes either a randomly chosen link, or the link carrying the strongest flux, or the link with the weakest flux, respectively. We study how the network structure and the total flux between randomly chosen source and drain nodes evolve. We discover a universal power-law decrease of the total flux, followed by an abrupt transport collapse. The time of collapse is shown to be determined by the average number of links per node in the initial network, highlighting the importance of this network property for ensuring safe and robust transport against random failures, intentional attacks and maintenance cost optimizations.
Nature
Pseudo-Darwinian evolution of physical flows in complex networks
Scientific Reports - Pseudo-Darwinian evolution of physical flows in complex networks
#articles Solvable delay model for epidemic spreading: the case of Covid-19 in Italy
Luca Dell’Anna
Scientific Reports volume 10, Article number: 15763 (2020)
Abstract
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in Italy, taking into account the containment measures implemented by the government in order to mitigate the spreading of the virus and the social costs for the population.
Luca Dell’Anna
Scientific Reports volume 10, Article number: 15763 (2020)
Abstract
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in Italy, taking into account the containment measures implemented by the government in order to mitigate the spreading of the virus and the social costs for the population.
Scientific Reports
Solvable delay model for epidemic spreading: the case of Covid-19 in Italy
Scientific Reports - <ArticleTitle Language="En" OutputMedium="All" xml:lang="en">Solvable delay model for epidemic spreading:...