Robustness of Network of Networks with Interdependent and Interconnected links

Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n networks with both interdependent and interconnected links is more complicated, and also more closely to real-life coupled network systems. Here we develop a framework to study analytically and numerically the robustness of this system. For the case of starlike network of n ER networks, we find that the system undergoes from second order to first order phase transition as coupling strength q increases. We find that increasing intra-connectivity links or inter-connectivity links can increase the robustness of the system, while the interdependency links decrease its robustness. Especially when q=1, we find exact analytical solutions of the giant component and the first order transition point. Understanding the robustness of network of networks with interdependent and interconnected links is helpful to design resilient infrastructures

Extrinsic models for the dielectric response of CaCu{3}Ti{4}O{12}

The large, temperature-independent, low-frequency dielectric constant recently observed in single-crystal CaCu{3}Ti{4}O{12} is most plausibly interpreted as arising from spatial inhomogenities of its local dielectric response. Probable sources of inhomogeneity are the various domain boundaries endemic in such materials: twin, Ca-ordering, and antiphase boundaries. The material in and neighboring such boundaries can be insulating or conducting. We construct a decision tree for the resulting six possible morphologies, and derive or present expressions for the dielectric constant for models of each morphology. We conclude that all six morphologies can yield dielectric behavior consistent with observations and suggest further experiments to distinguish among them.Comment: 9 pages, with 1 postscript figure embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/mc_ext/index.htm

Singlet-triplet splitting, correlation and entanglement of two electrons in quantum dot molecules

Starting with an accurate pseudopotential description of the single-particle states, and following by configuration-interaction treatment of correlated electrons in vertically coupled, self-assembled InAs/GaAs quantum dot-molecules, we show how simpler, popularly-practiced approximations, depict the basic physical characteristics including the singlet-triplet splitting, degree of entanglement (DOE) and correlation. The mean-field-like single-configuration approaches such as Hartree-Fock and local spin density, lacking correlation, incorrectly identify the ground state symmetry and give inaccurate values for the singlet-triplet splitting and the DOE. The Hubbard model gives qualitatively correct results for the ground state symmetry and singlet-triplet splitting, but produces significant errors in the DOE because it ignores the fact that the strain is asymmetric even if the dots within a molecule are identical. Finally, the Heisenberg model gives qualitatively correct ground state symmetry and singlet-triplet splitting only for rather large inter-dot separations, but it greatly overestimates the DOE as a consequence of ignoring the electron double occupancy effect.Comment: 13 pages, 9 figures. To appear in Phys. Rev.

Percolation on interacting networks with feedback-dependency links

When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting networks with feedback-dependency links. We find that when nodes of between networks are lowly connected, the system undergoes from second order transition through hybrid order transition to first order transition as coupling strength increases. And, as average degree of each inter-network increases, first order region becomes smaller and second-order region becomes larger but hybrid order region almost keep constant. Especially, the results implies that average degree \bar{k} between intra-networks has a little influence on robustness of system for weak coupling strength, but for strong coupling strength corresponding to first order transition system become robust as \bar{k} increases. However, when average degree k of inter-network is increased, the system become robust for all coupling strength. Additionally, when nodes of between networks are highly connected, the hybrid order region disappears and the system first order region becomes larger and secondorder region becomes smaller. Moreover, we find that the existence of feedback dependency links between interconnecting networks makes the system extremely vulnerable by comparing non-feedback condition for the same parameters.First author draf

Does"good government"draw foreign capital ? Explaining China's exceptional foreign direct investment inflow

China is now the world's largest destination of foreign direct investment (FDI), despite assessments highlighting its institutional deficiencies. But this FDI inflow corresponds closely to predicted FDI flows into China from a model that predicts FDI inflow based on government quality indicators and controls and is estimated across a sample of other weak-institution countries. The only real discrepancy is that, if government quality is measured by constraints on executive power, China receives somewhat more FDI than the model predicts. This might reflect an underestimation of the strength of these constraints in China, a unique institutional setting for FDI operations, FDI based on expected future institutional improvements, or a unique Chinese model of development. The authors conclude that Ockham's razor disfavors the last. They also note that FDI may be elevated because Chinese institutions protect foreign firms better than domestic ones.Foreign Direct Investment,Economic Theory&Research,Legal Products,Investment and Investment Climate,Parliamentary Government

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution $P(k)\sim exp[-\lambda (k-2\rho-2)], \lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,...$, independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the H$\acute{e}$non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series.Comment: 23 pages, 12 figure

Scaling Dark Energy in a Five-Dimensional Bouncing Cosmological Model

We consider a 5-dimensional Ricci flat bouncing cosmological model in which the 4-dimensional induced matter contains two components at late times - the cold dark matter (CDM)+baryons and dark energy. We find that the arbitrary function $f(z)$ contained in the solution plays a similar role as the potential $V(\phi)$ in quintessence and phantom dark energy models. To resolve the coincidence problem, it is generally believed that there is a scaling stage in the evolution of the universe. We analyze the condition for this stage and show that a hyperbolic form of the function $f(z)$ can work well in this property. We find that during the scaling stage (before $z\approx 2$), the dark energy behaves like (but not identical to) a cold dark matter with an adiabatic sound speed $c_{s}^{2}\approx 0$ and $p_{x}\approx 0$. After $z\approx 2$, the pressure of dark energy becomes negative. The transition from deceleration to acceleration happens at $z_{T}\approx 0.8$ which, as well as other predictions of the $5D$ model, agree with current observations.Comment: 13 pages, 1 table, 3 figures, published version, references adde