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

Apparent electron-phonon interaction in strongly correlated systems

We study the interaction of electrons with phonons in strongly correlated solids, having high-T_c cuprates in mind. Using sum-rules, we show that the apparent strength of this interaction strongly depends on the property studied. If the solid has a small fraction (doping) delta of charge carriers, the influence of the interaction on the phonon self-energy is reduced by a factor delta, while there is no corresponding reduction of the coupling seen in the electron self-energy. This supports the interpretation of recent photoemission experiments, assuming a strong coupling to phonons.Comment: 4 pages, RevTeX, 2 eps figure

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

Electron-phonon interaction in the t-J model

We derive a t-J model with electron-phonon coupling from the three-band model, considering modulation of both hopping and Coulomb integrals by phonons. While the modulation of the hopping integrals dominates, the modulation of the Coulomb integrals cannot be neglected. The model explains the experimentally observed anomalous softening of the half-breathing mode upon doping and a weaker softening of the breathing mode. It is shown that other phonons are not strongly influenced, and, in particular, the coupling to a buckling mode is not strong in this model.Comment: 4 pages, RevTeX, 3 eps figures; final version with minor correction

Assessing the skill of football players using statistical methods

Professional football is a business worth billions of pounds a year. Player recruitment is a key aspect of the business with expenditures directly related to it (in the form of transfer fees and wages) accounting for the majority of clubs’ budgets. The purpose of this study is to propose methods to assist player evaluation based on statistical modelling that could be used to support recruitment decisions. In this thesis we argue that if such methods are to serve as the basis of player valuation, they need to have predictive utility, since it is players’ future performance that clubs benefit from and thus should be paying for. We present examples of how simplistic approaches to quantifying a footballer’s skill lack such predictive character.The original contribution of this thesis is a framework for evaluating footballers’ worth to a team in terms of their expected contribution to its results. The framework attempts to address one of the key difficulties in modelling the game of football, i.e. its free-flowing nature, by discretising it into a series of events. The evolution of the game from one event to another is described using a Markov chain model in which each game is described by a specific transition matrix with elements depending on the skills of the players involved in this game. Based on this matrix it is possible to calculate game outcome related metrics such as expected goals difference between the two teams at the end of the game. It enables us to establish a link between a specific skill of a givenplayer and the game outcome. The skill estimates come from separate, location specific, models, e.g. the shooting skill for each player is estimated in a model of converting shots to goals given the shot location. We demonstrate how recognising the involvement of random chance in individualperformance, together with accounting for the environment in which the evaluated performance occurred, gives our statistical model a predictive advantage when comparedto naive methods which simply extrapolate past performance. This predictive advantage is shown to be present when passing and shooting skills are evaluated in isolation, as well as when measures of passing and shooting skills are combined in the proposed comprehensive metric of player’s expected contribution to the success of a team

Propagation of a hole on a Neel background

We analyze the motion of a single hole on a N\'eel background, neglecting spin fluctuations. Brinkman and Rice studied this problem on a cubic lattice, introducing the retraceable-path approximation for the hole Green's function, exact in a one-dimensional lattice. Metzner et al. showed that the approximationalso becomes exact in the infinite-dimensional limit. We introduce a new approach to this problem by resumming the Nagaoka expansion of the propagator in terms of non-retraceable skeleton-paths dressed by retraceable-path insertions. This resummation opens the way to an almost quantitative solution of the problemin all dimensions and, in particular sheds new light on the question of the position of the band-edges. We studied the motion of the hole on a double chain and a square lattice, for which deviations from the retraceable-path approximation are expected to be most pronounced. The density of states is mostly adequately accounted for by the retra\-ce\-able-path approximation. Our band-edge determination points towards an absence of band tails extending to the Nagaoka energy in the spectrums of the double chain and the square lattice. We also evaluated the spectral density and the self-energy, exhibiting k-dependence due to finite dimensionality. We find good agreement with recent numerical results obtained by Sorella et al. with the Lanczos spectra decoding method. The method we employ enables us to identify the hole paths which are responsible for the various features present in the density of states and the spectral density.Comment: 26 pages,Revte

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

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]