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

Controlling shot noise in double-barrier magnetic tunnel junctions

We demonstrate that shot noise in Fe/MgO/Fe/MgO/Fe double-barrier magnetic tunnel junctions is determined by the relative magnetic configuration of the junction and also by the asymmetry of the barriers. The proposed theoretical model, based on sequential tunneling through the system and including spin relaxation, successfully accounts for the experimental observations for bias voltages below 0.5V, where the influence of quantum well states is negligible. A weak enhancement of conductance and shot noise, observed at some voltages (especially above 0.5V), indicates the formation of quantum well states in the middle magnetic layer. The observed results open up new perspectives for a reliable magnetic control of the most fundamental noise in spintronic structures.Comment: 8 pages, 4 figure

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]

Reduction of three-band model for copper oxides to single-band generalized t~-~J model

A three-band model for copper oxides in the region of parameters where the second hole on the copper has energy close to the first hole on the oxygen is considered. The exact solution for one hole on a ferromagnetic background of the ordered copper spins is obtained. A general procedure for transformation of the primary Hamiltonian to the Hamiltonian of singlet and triplet excitations is proposed. Reduction of the singlet-triplet Hamiltonian to the single-band Hamiltonian of the generalized t~-~J model is performed. A comparison of the solution for the generalized t~-~J model on a ferromagnetic background with the exact solution shows a very good agreement.Comment: 20 pages (LATEX

Spatial Structure of Spin Polarons in the t-J Model

The deformation of the quantum Neel state induced by a spin polaron is analyzed in a slave fermion approach. Our method is based on the selfconsistent Born approximation for Green's and the wave function for the quasiparticle. The results of various spin-correlation functions relative to the position of the moving hole are discussed and shown to agree with those available from small cluster calculations. Antiferromagnetic correlations in the direct neighborhood of the hole are reduced, but they remain antiferromagnetic even for J as small as 0.1 t. These correlation functions exhibit dipolar distortions in the spin structure, which sensitively depend on the momentum of the quasiparticle. Their asymptotic decay with the distance from the hole is governed by power laws, yet the spectral weight of the quasiparticles does not vanish.Comment: 12 pages, 2 postscipt files with figures; uses REVTeX, to be published in Phys. Rev. B, Feb. 199

Fatigue behaviour of SiC p -reinforced aluminium composites in the very high cycle regime using ultrasonic fatigue

The fatigue behaviour of a 2009/SiC/15p-T4 DRA composite has been examined in the very high cycle fatigue (VHCF) regime where 10 7 ≤ N f ≤ 10 9 cycles. Ultrasonic fatigue was used to achieve the very high cycle counts. Careful processing yielded a composite with a very homogeneous particle distribution with minimal clustering. Fatigue crack initiation was observed almost exclusively at AlCuFe inclusions with no crack initiation observed at SiC particle clusters. Fatigue lives at a given stress level exhibited minimal scatter and subsurface crack initiation was observed in all cases. This behaviour is consistent with the presence of a low number density of critical inclusions that are responsible for crack initiation very early in fatigue life.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73177/1/j.1460-2695.2006.00998.x.pd