Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that
the damage in the network due to a failure is a continuous function of the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of $n$ classic ErdH{o}s-R{e}nyi (ER) networks, where each network depends on the same number $m$ of other networks, i.e., a random regular network of interdependent ER networks. In contrast to a emph{treelike} NetONet in which the size of the largest connected cluster (mutual component) depends on $n$, the loops in the RR NetONet cause the largest connected cluster to depend only on $m$. We also analyzed the extremely vulnerable feedback condition of coupling. In the case of ER networks, the NetONet only exhibits two phases, a second order phase transition and collapse, and there is no first phase transition regime unlike the no feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when $q$ is large and second order phase transition when $q$ is small. Our results can help in designing robust interdependent systems.
There is a long standing debate over how to objectively compare the career achievements of professional athletes from different historical eras. Developing an objective approach will be of particular importance over the next decade as Major League Ba
seball (MLB) players from the steroids era become eligible for Hall of Fame induction. Here we address this issue, as well as the general problem of comparing statistics from distinct eras, by detrending the seasonal statistics of professional baseball players. We detrend player statistics by normalizing achievements to seasonal averages, which accounts for changes in relative player ability resulting from both exogenous and endogenous factors, such as talent dilution from expansion, equipment and training improvements, as well as performance enhancing drugs (PED). In this paper we compare the probability density function (pdf) of detrended career statistics to the pdf of raw career statistics for five statistical categories -- hits (H), home runs (HR), runs batted in (RBI), wins (W) and strikeouts (K) -- over the 90-year period 1920-2009. We find that the functional form of these pdfs are stationary under detrending. This stationarity implies that the statistical regularity observed in the right-skewed distributions for longevity and success in professional baseball arises from both the wide range of intrinsic talent among athletes and the underlying nature of competition. Using this simple detrending technique, we examine the top 50 all-time careers for H, HR, RBI, W and K. We fit the pdfs for career success by the Gamma distribution in order to calculate objective benchmarks based on extreme statistics which can be used for the identification of extraordinary careers.
Publication statistics are ubiquitous in the ratings of scientific achievement, with citation counts and paper tallies factoring into an individuals consideration for postdoctoral positions, junior faculty, tenure, and even visa status for internatio
nal scientists. Citation statistics are designed to quantify individual career achievement, both at the level of a single publication, and over an individuals entire career. While some academic careers are defined by a few significant papers (possibly out of many), other academic careers are defined by the cumulative contribution made by the authors publications to the body of science. Several metrics have been formulated to quantify an individuals publication career, yet none of these metrics account for the dependence of citation counts and journal size on time. In this paper, we normalize publication metrics across both time and discipline in order to achieve a universal framework for analyzing and comparing scientific achievement. We study the publication careers of individual authors over the 50-year period 1958-2008 within six high-impact journals: CELL, the New England Journal of Medicine (NEJM), Nature, the Proceedings of the National Academy of Science (PNAS), Physical Review Letters (PRL), and Science. In comparing the achievement of authors within each journal, we uncover quantifiable statistical regularity in the probability density function (pdf) of scientific achievement across both time and discipline. The universal distribution of career success within these arenas for publication raises the possibility that a fundamental driving force underlying scientific achievement is the competitive nature of scientific advancement.
Four scenarios have been proposed for the low--temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism which leads to each is debated. Moreover, it is still unclear which of the scenarios best desc
ribes water, as there is no definitive experimental test. Here we address both open issues within the framework of a microscopic cell model by performing a study combining mean field calculations and Monte Carlo simulations. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. We argue that our conclusions are model-independent. Using estimates from experimental data for H bond properties the model predicts that the low-temperature phase diagram of water exhibits a liquid--liquid critical point at positive pressure.
We investigate the traffic flows of the Korean highway system, which contains both public and private transportation information. We find that the traffic flow T(ij) between city i and j forms a gravity model, the metaphor of physical gravity as desc
ribed in Newtons law of gravity, P(i)P(j)/r(ij)^2, where P(i) represents the population of city i and r(ij) the distance between cities i and j. It is also shown that the highway network has a heavy tail even though the road network is a rather uniform and homogeneous one. Compared to the highway network, air and public ground transportation establish inhomogeneous systems and have power-law behaviors.
