Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely believed that cr
itical points are difficult to estimate, and it is even more difficult, if not impossible, to predict the time such transitions occur [1-4]. We analyze a class of decaying dynamical networks experiencing persistent attacks in which the magnitude of the attack is quantified by the probability of an internal failure, and there is some chance that an internal failure will be permanent. When the fraction of active neighbors declines to a critical threshold, cascading failures trigger a network breakdown. For this class of network we find both numerically and analytically that the time to the network breakdown, equivalent to the network lifetime, is inversely dependent upon the magnitude of the attack and logarithmically dependent on the threshold. We analyze how permanent attacks affect dynamical network robustness and use the network lifetime as a measure of dynamical network robustness offering new methodological insight into system dynamics.
The description of the $eta$ and $eta^prime$ mesons in the Dyson-Schwinger approach has relied on the Witten-Veneziano relation. The present paper explores the consequences of using instead its generalization recently proposed by Shore. On the exampl
es of three different model interactions, we find that irrespective of the concrete model dynamics, our Dyson-Schwinger approach is phenomenologically more successful in conjunction with the standard Witten-Veneziano relation than with the proposed generalization valid in all orders in the $1/N_c$ expansion.
Most of model considerations of the hidden nucleon strangeness, as well as some preliminary experimental evidence, led to the expectations of relatively sizeable strange vector form factors of the proton. For example, it seemed that the contribution
of the fluctuating strange quark-antiquark pairs accounts for as much as one tenth of the protons magnetic moment. By the same token, baryon models which failed to produce the vector strangeness of the nucleon seemed disfavored. Recently, however, more accurate measurements and more sophisticated data analysis, as well as lattice simulations, revealed that the form factors associated with the vector strangeness of the nucleon are much smaller than thought previously; in fact, due to the experimental uncertainties, the measured strange vector-current proton form factors may be consistent with zero. In the light of that, we re-asses the merit of the baryon models leading to little or no vector strangeness of the nucleon. It is done on the concrete example of the baryon model which essentially amounts to the MIT bag enriched by the diluted instanton liquid.
