Players Indifferent to Cooperate and Characterizations of the Shapley Value

In this paper we provide new axiomatizations of the Shapley value for TU-games using axioms that are based on relational aspects in the interactions among players. Some of these relational aspects, in particular the economic or social interest of each player in cooperating with each other, can be found embedded in the characteristic function. We define a particular relation among the players that it is based on mutual indifference. The first newaxiom expresses that the payoffs of two playerswho are not indifferent to each other are affected in the same way if they become enemies and do not cooperate with each other anymore. The second new axiom expresses that the payoff of a player is not affected if players to whom it is indifferent leave the game. We show that the Shapley value is characterized by these two axioms together with the well-known efficiency axiom. Further, we show that another axiomatization of the Shapley value is obtained if we replace the second axiom and efficiency by the axiom which applies the efficiency condition to every class of indifferent players. Finally, we extend the previous results to the case of weighted Shapley values. © Springer-Verlag Berlin Heidelberg 2012

Doping dependence of magnetic excitations of 1D cuprates as probed by Resonant Inelastic x-ray Scattering

We study the dynamical, momentum dependent two- and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t-J$ system the four-spin response vanishes at $\pi$, whereas the two-spin correlator is peaked around $\pi/2$, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at $\pi$ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta the higher-energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.Comment: 7 pages, 5 figure

Theory for Magnetism and Triplet Superconductivity in LiFeAs

Superconducting pnictides are widely found to feature spin-singlet pairing in the vicinity of an antiferromagnetic phase, for which nesting between electron and hole Fermi surfaces is crucial. LiFeAs differs from the other pnictides by (i) poor nesting properties and (ii) unusually shallow hole pockets. Investigating magnetic and pairing instabilities in an electronic model that incorporates these differences, we find antiferromagnetic order to be absent. Instead we observe almost ferromagnetic fluctuations which drive an instability toward spin-triplet p-wave superconductivity.Comment: Published versio

Community Schools Unfolded: A review of the literature.

Community schools are quickly increasing in number, but there is no evidence whether they are more effective than traditional schools. No study has empirically compared community schools to other schools. This study reviews the literature on the effectiveness of community schools. We focus on their three main components: cooperation with external organizations, parental involvement, and extracurricular activities. This review indicates that involving external organizations seems valuable in terms of social cohesion in neighborhoods. Parental involvement is particularly important for the educational development of lower socio-economic status families. Extracurricular activities positively relate to students? development in academic and social terms.