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.
In order to model volatile real-world network behavior, we analyze phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects phase-fli
pping dynamics, and find the probability that no more than q% of nodes and links fail. We derive higher moments of the fractions of active nodes and active links, $f_n(t)$ and $f_{ell}(t)$, and define two estimators to quantify the level of risk in a network. We find hysteresis in the correlations of $f_n(t)$ due to failures at the node level, and derive conditional probabilities for phase-flipping in networks. We apply our model to economic and traffic networks.
Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its {it per capita} GDP ({it gdp}) rank within a decade follows an exponential distribution with decay constant $lam
bda = 0.12$. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as $lambda$, suggesting that the dynamics of {it gdp}, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economys competitiveness relative to its {it gdp}. For all European and EU countries during the 2008-2011 economic downturn we find that the drop in {it gdp} in more competitive countries relative to {it gdp} was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers.
We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor-the debt-to-asset ratio R-in order to study the stability of the Zipf distribution o
f R over time. We find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, we employ Bayess theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value. For 2,737 bankrupt firms, we demonstrate size dependence in assets change during the bankruptcy proceedings. Prepetition firm assets and petition firm assets follow Zipf distributions but with different exponents, meaning that firms with smaller assets adjust their assets more than firms with larger assets during the bankruptcy process. We compare bankrupt firms with nonbankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 New York Stock Exchange (NYSE) members. We find that both assets and liabilities follow a Pareto distribution. The finding is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees-although the market capitalization of Nasdaq stocks follows a Pareto distribution, the same distribution does not describe NYSE stocks. We propose a coupled Simon model that simultaneously evolves both assets and debt with the possibility of bankruptcy, and we also consider the possibility of firm mergers.
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.
In order to investigate whether government regulations against corruption can affect the economic growth of a country, we analyze the dependence between Gross Domestic Product (GDP) per capita growth rates and changes in the Corruption Perceptions In
dex (CPI). For the period 1999-2004 on average for all countries in the world, we find that an increase of CPI by one unit leads to an increase of the annual GDP per capita by 1.7 %. By regressing only European transition countries, we find that $Delta$CPI = 1 generates increase of the annual GDP per capita by 2.4 %. We also analyze the relation between foreign direct investments received by different countries and CPI, and we find a statistically significant power-law functional dependence between foreign direct investment per capita and the country corruption level measured by the CPI. We introduce a new measure to quantify the relative corruption between countries based on their respective wealth as measured by GDP per capita.
