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

Efficacy of B-cell-targeted therapy with rituximab in patients with rheumatoid arthritis.

BACKGROUND: An open-label study indicated that selective depletion of B cells with the use of rituximab led to sustained clinical improvements for patients with rheumatoid arthritis. To confirm these observations, we conducted a randomized, double-blind, controlled study. METHODS: We randomly assigned 161 patients who had active rheumatoid arthritis despite treatment with methotrexate to receive one of four treatments: oral methotrexate (> or =10 mg per week) (control); rituximab (1000 mg on days 1 and 15); rituximab plus cyclophosphamide (750 mg on days 3 and 17); or rituximab plus methotrexate. Responses defined according to the criteria of the American College of Rheumatology (ACR) and the European League against Rheumatism (EULAR) were assessed at week 24 (primary analyses) and week 48 (exploratory analyses). RESULTS: At week 24, the proportion of patients with 50 percent improvement in disease symptoms according to the ACR criteria, the primary end point, was significantly greater with the rituximab-methotrexate combination (43 percent, P=0.005) and the rituximab-cyclophosphamide combination (41 percent, P=0.005) than with methotrexate alone (13 percent). In all groups treated with rituximab, a significantly higher proportion of patients had a 20 percent improvement in disease symptoms according to the ACR criteria (65 to 76 percent vs. 38 percent, P< or =0.025) or had EULAR responses (83 to 85 percent vs. 50 percent, P< or =0.004). All ACR responses were maintained at week 48 in the rituximab-methotrexate group. The majority of adverse events occurred with the first rituximab infusion: at 24 weeks, serious infections occurred in one patient (2.5 percent) in the control group and in four patients (3.3 percent) in the rituximab groups. Peripheral-blood immunoglobulin concentrations remained within normal ranges. CONCLUSIONS: In patients with active rheumatoid arthritis despite methotrexate treatment, a single course of two infusions of rituximab, alone or in combination with either cyclophosphamide or continued methotrexate, provided significant improvement in disease symptoms at both weeks 24 and 48

Effects of Next-Nearest-Neighbor Hopping on the Hole Motion in an Antiferromagnetic Background

In this paper we study the effect of next-nearest-neighbor hopping on the dynamics of a single hole in an antiferromagnetic (N\'{e}el) background. In the framework of large dimensions the Green function of a hole can be obtained exactly. The exact density of states of a hole is thus calculated in large dimensions and on a Bethe lattice with large coordination number. We suggest a physically motivated generalization to finite dimensions (e.g., 2 and 3). In $d=2$ we present also the momentum dependent spectral function. With varying degree, depending on the underlying lattice involved, the discrete spectrum for holes is replaced by a continuum background and a few resonances at the low energy end. The latter are the remanents of the bound states of the $t-J$ model. Their behavior is still largely governed by the parameters $t$ and $J$. The continuum excitations are more sensitive to the energy scales $t$ and $t_1$.Comment: To appear in Phys. Rev. B, Revtex, 23 pages, 10 figures available on request from [email protected]

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

Theory of Dynamic Stripe Induced Superconductivity

Since the recently reported giant isotope effect on T* [1] could be consistently explained within an anharmonic spin-charge-phonon interaction model, we consider here the role played by stripe formation on the superconducting properties within the same model. This is a two-component scenario and we recast its basic elements into a BCS effective Hamiltonian. We find that the stripe formation is vital to high-Tc superconductivity since it provides the glue between the two components to enhance Tc to the unexpectedly large values observed experimentally.Comment: 7 pages, 2 figure

Hole-Hole Contact Interaction in the t-J Model

Using an analytical variational approach we calculate the hole-hole contact interaction on the N\'{e}el background. Solution of the Bethe-Salpeter equation with this interaction gives bound states in $d$- and p-waves with binding energies close to those obtained by numerical methods. At $t/J \ge 2-3$ the bound state disappears. In conclusion we discuss the relation between short range and long range interactions and analogy with the problem of pion condensation in nuclear matter.Comment: 11 pp. (LATEX), 7 figures (PostScript) appended, report N

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

Green Function Monte Carlo with Stochastic Reconfiguration: an effective remedy for the sign problem disease

A recent technique, proposed to alleviate the ``sign problem disease'', is discussed in details. As well known the ground state of a given Hamiltonian $H$ can be obtained by applying the imaginary time propagator $e^{-H \tau}$ to a given trial state $\psi_T$ for large imaginary time $\tau$ and sampling statistically the propagated state $\psi_{\tau} = e^{-H \tau} \psi_T$. However the so called ``sign problem'' may appear in the simulation and such statistical propagation would be practically impossible without employing some approximation such as the well known ``fixed node'' approximation (FN). This method allows to improve the FN dynamic with a systematic correction scheme. This is possible by the simple requirement that, after a short imaginary time propagation via the FN dynamic, a number $p$ of correlation functions can be further constrained to be {\em exact} by small perturbation of the FN propagated state, which is free of the sign problem. By iterating this scheme the Monte Carlo average sign, which is almost zero when there is sign problem, remains stable and finite even for large $\tau$. The proposed algorithm is tested against the exact diagonalization results available on finite lattice. It is also shown in few test cases that the dependence of the results upon the few parameters entering the stochastic technique can be very easily controlled, unless for exceptional cases.Comment: 44 pages, RevTeX + 5 encaplulated postscript figure