The average tree solution for multi-choice forest games

In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et?al. (Games Econ. Behav. 62:77?C92, 2008) for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange in J. Polit. Econ. 112:754?C778, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution.     

Derivation of the near-surface dielectric function of amorphous silicon from photoelectron loss spectra

The near-surface dielectric function ε(?ω) of hydrogenated amorphous silicon (a-Si:H) films has been derived from X-ray photoelectron energy-loss spectra, over the energy range 0–40 eV. Removal of low lying single-electron excitations is a prerequisite step to proceed to the derivation of the single plasmon energy loss function Im[? 1/ε(?ω)] due to collective electron oscillations. Several methods are compared to separate interband transitions from bulk or surface plasmons excitation. The shape of interband excitation loss in the range 1–10 eV can be described by a Henke function; alternatively, its removal using a sigmoid weighting function is a low-noise and reliable method. After deconvolution of multiple plasmon losses and self-consistent elimination of surface plasmon excitation, the single plasmon loss distribution allows recovery of optical (ellipsometry) data measured in the near-UV to visible range.     

Compensations in the Shapley value and the compensation solutions for graph games

We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition he does not belong to. We give a representation in terms of formation of the grand coalition according to an ordering of the players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication graph in order to construct new allocation rules called the compensation solutions. Firstly, we consider cooperative games with arbitrary graphs and construct rooted spanning trees (see Demange, J Political Econ 112:754–778, 2004) instead of orderings of the players by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively. Secondly, we consider cooperative games with a forest (cycle-free graph) and all its rooted spanning trees. The compensation solution is characterized by component efficiency and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component in the communication graph.     

Surface energy and hybridization studies of amorphous carbon surfaces

Surface properties of a large number of amorphous carbon (a-C) films have been investigated using contact angle measurements and X-ray photoelectron spectroscopy (XPS). Dense a-C surfaces with variable sp³/(sp² + sp³) average hybridization were grown using sputtering or pulsed laser deposition (PLD) and were further chemically modified by thermal annealing, ion bombardment or covalent grafting of organic monolayers. The average carbon hybridization, impurity level and mass density, were deduced from XPS and photoelectron energy loss spectroscopy (PEELS). The depth sensitivity of the dispersive (Lifshitz–van der Waals) interaction, estimated at 1–2 nm from the dependence of γ^LW on the grafted perflorodecene molecule coverage, is much better than XPS which probes a 3–5 nm depth. The observation of a non-monotonic behavior in the correlation between surface hybridization and electron donor component of surface energy reveals that the average carbon hybridization alone does not describe the entire surface energy physics. The role of π bond clustering in the polar interactions is thus considered and some implications on surface reactivity and mutual interactions with molecular or biomolecular species are discussed.