Efficient computation of the Shapley value for game-theoretic network centrality

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo

Anomalous Spin and Charge Dynamics of the 2D t-J Model at low doping

We present an exact diagonalization study of the dynamical spin and density correlation function of the 2D t-J model for hole doping < 25%. Both correlation functions show a remarkably regular, but completely different scaling behaviour with both hole concentration and parameter values: the density correlation function is consistent with that of bosons corresponding to the doped holes and condensed into the lowest state of the noninteracting band of width 8t, the spin correlation function is consistent with Fermions in a band of width J. We show that the spin bag picture gives a natural explanation for this unusual behaviour.Comment: Revtex-file, 4 PRB pages + 5 figures attached as uu-encoded ps-files Hardcopies of figures (or the entire manuscript) can also be obtained by e-mailing to: [email protected]

AWG-based photonic transmitter with DBR mirrors and Mach-Zehnder modulators

In this letter, we demonstrate a novel monolithically integrated photonic multiwavelength transmitter that was realized by integrating an arrayed waveguide grating-based laser with selective distributed Bragg reflector mirrors and Mach-Zehnder modulators. The integrated circuit was designed according to a generic integration model, by utilizing standardized photonic building blocks, and was fabricated on an InP-based platform in a multiproject wafer run. The device delivers above 1 mW of optical power into the fiber with a side mode suppression ratio better than 40 dB. The linewidth of the generated signals is 275 kHz. We achieved error free 50-km transmission at the modulation data rate of 10 Gb/s per channel, for a received power of -26.5 dBm

Hubbard model versus t-J model: The one-particle spectrum

The origin of the apparent discrepancies between the one-particle spectra of the Hubbard and t-J models is revealed: Wavefunction corrections, in addition to the three-site terms, should supplement the bare t-J. In this way a quantitative agreement between the two models is obtained, even for the intermediate-$U$ values appropriate for the high-Tc cuprate superconductors. Numerical results for clusters of up to 20 sites are presented. The momentum dependence of the observed intensities in the photoemission spectra of Sr2CuO2Cl2 are well described by this complete strong-coupling approach.Comment: 4 two-column RevTeX pages, including 4 Postscript figures. Uses epsf. Accepted for publication in Physical Review B, Rapid Communicatio

Spin and Charge Texture around In-Plane Charge Centers in the CuO_2 planes

Recent experiments on La_2Cu_{1-x}Li_xO_4 show that although the doped holes remain localized near the substitutional Li impurities, magnetic order is rapidly suppressed. An examination of the spin texture around a bound hole in a CuO_2 plane shows that the formation of a skyrmion is favored in a wide range of parameters, as was previously proposed in the context of Sr doping. The spin texture may be observable by elastic diffuse neutron scattering, and may also have a considerable effect on NMR lineshapes.Comment: 4 pages, postscript file, hardcopy available upon request, to appear in PR

Unifying the Phase Diagrams of the Magnetic and Transport Properties of La_(2-x)Sr_xCuO_4, 0 < x < 0.05

An extensive experimental and theoretical effort has led to a largely complete mapping of the magnetic phase diagram of La_(2-x)Sr_xCuO_4, and a microscopic model of the spin textures produced in the x < 0.05 regime has been shown to be in agreement with this phase diagram. Here we use this same model to derive a theory of the impurity-dominated, low temperature transport. Then, we present an analysis of previously published data for two samples: x = 0.002 data from Chen et. al., and x = 0.04 data from Keimer et. al. We show that the transport mechanisms in the two systems are the same, even though they are on opposite sides of the observed insulator-to-metal transition. Our model of impurity effects on the impurity band conduction, variable-range hopping conduction, and coulomb gap conduction, is similar to that used to describe doped semiconductors. However, for La_(2-x)Sr_xCuO_4 we find that in addition to impurity-generated disorder effects, strong correlations are important and must be treated on a equal level with disorder. On the basis of this work we propose a phase diagram that is consistent with available magnetic and transport experiments, and which connects the undoped parent compound with the lowest x value for which La_(2-x)Sr_xCuO_4 is found to be superconducting, x about 0.06.Comment: 7 pages revtex with one .ps figur

Interaction of a Magnetic Impurity with Strongly Correlated Conduction Electrons

We consider a magnetic impurity which interacts by hybridization with a system of strongly correlated conduction electrons. The latter are described by a Hubbard Hamiltonian. By means of a canconical transformation the charge degrees of freedom of the magnetic impurity are eliminated. The resulting effective Hamiltonian $H_{\rm eff}$ is investigated and various limiting cases are considered. If the Hubbard interaction $U$ between the conduction electrons is neglected $H_{\rm eff}$ reduces to a form obtained by the Schrieffer-Wolff transformation, which is essentially the Kondo Hamiltonian. If $U$ is large and the correlations are strong $H_{\rm eff}$ is changed. One modification concerns the coefficient of the dominant exchange coupling of the magnetic impurity with the nearest lattice site. When the system is hole doped, there is also an antiferromagnetic coupling to the nearest neighbors of that site involving additionally a hole. Furthermore, it is found that the magnetic impurity attracts a hole. In the case of electron doping, double occupancies are repelled by the impurity. In contrast to the hole-doped case, we find no magnetic coupling which additionally involves a doubly occupied site.Comment: 16 pages, Revtex 3.