We analyze a network formation game in a strategic setting where payoffs of individuals depend only on their immediate neighbourhood. We call these payoffs as localized payoffs. In this game, the payoff of each individual captures (1) the gain from i
mmediate neighbors, (2) the bridging benefits, and (3) the cost to form links. This implies that the payoff of each individual can be computed using only its single-hop neighbourhood information. Based on this simple model of network formation, our study explores the structure of networks that form, satisfying one or both of the properties, namely, pairwise stability and efficiency. We analytically prove the pairwise stability of several interesting network structures, notably, the complete bi-partite network, complete equi-k-partite network, complete network and cycle network, under various configurations of the model. We validate and extend these results through extensive simulations. We characterize topologies of efficient networks by drawing upon classical results from extremal graph theory and discover that the Turan graph (or the complete equi-bi-partite network) is the unique efficient network under many configurations of parameters. We examine the tradeoffs between topologies of pairwise stable networks and efficient networks using the notion of price of stability, which is the ratio of the sum of payoffs of the players in an optimal pairwise stable network to that of an efficient network. Interestingly, we find that price of stability is equal to 1 for almost all configurations of parameters in the proposed model; and for the rest of the configurations of the parameters, we obtain a lower bound of 0.5 on the price of stability. This leads to another key insight of this paper: under mild conditions, efficient networks will form when strategic individuals choose to add or delete links based on only localized payoffs.
We report an experimental and theoretical analysis of the sqrt(3)x sqrt(3)-R30 and 2x2 reconstructions on the NiO (111) surface combining transmission electron microscopy, x-ray photoelectron spectroscopy, and reasonably accurate density functional c
alculations using the meta-GGA hybrid functional TPSSh. While the main focus here is on the surface structure, we also observe an unusual step morphology with terraces containing only even numbers of unit cells during annealing of the surfaces. The experimental data clearly shows that the surfaces contain significant coverage of hydroxyl terminations, and the surface structures are essentially the same as those reported on the MgO (111) surface implying an identical kinetically-limited water-driven structural transition pathway. The octapole structure can therefore be all but ruled out for single crystals of NiO annealed in or transported through humid air. . The theoretical analysis indicates, as expected, that simple density functional theory methods for such strongly-correlated oxide surfaces are marginal, while better consideration of the metal d-electrons has a large effect although, it is still not perfect.
We report an experimental refinement of the local charge density at the Si (111) 7x7 surface utilizing a combination of x-ray and high energy electron diffraction. By perturbing about a bond-centered pseudoatom model, we find experimentally that the
adatoms are in an anti-bonding state with the atoms directly below. We are also able to experimentally refine a charge transfer of 0.26(4) e- from each adatom site to the underlying layers. These results are compared with a full-potential all-electron density functional DFT calculation.
We report an experimental and theoretical analysis of the root(3)xroot(3)-R30 and 2x2 reconstructions on the MgO (111) surface combining transmission electron microscopy, x-ray photoelectron spectroscopy, and reasonably accurate density functional ca
lculations using the meta-GGA functional TPSS. The experimental data clearly shows that the surfaces contain significant coverages of hydroxyl terminations, even after UHV annealing, and as such cannot be the structures which have been previously reported. For the 2x2 surfaces a relatively simple structural framework is detailed which fits all the experimental and theoretical data. For the root(3)xroot(3) there turn out to be two plausible structures and neither the experimental nor theoretical results can differentiate between the two within error. However, by examining the conditions under which the surface is formed we describe a kinetic route for the transformation between the different reconstructions that involves mobile hydroxyl groups and protons, and relatively immobile cations, which strongly suggests only one of the two root(3)xroot(3) structures.
The recent quest for improved functional materials like high permittivity dielectrics and/or multiferroics has triggered an intense wave of research. Many materials have been checked for their dielectric permittivity or their polarization state. In t
his report, we call for caution when samples are simultaneously displaying insulating behavior and defect-related conductivity. Many oxides containing mixed valent cations or oxygen vacancies fall in this category. In such cases, most of standard experiments may result in effective high dielectric permittivity which cannot be related to ferroelectric polarization. Here we list few examples of possible discrepancies between measured parameters and their expected microscopic origin.
