The Owen and Banzhaf–Owen values revisited

In this work, we consider games with coalitional structure. We afford two new parallel axiomatic characterizations for the well-known Owen and Banzhaf–Owen coalitional values. Two properties are common to both characterizations: a property of balanced contributions and a property of neutrality. The results prove that the main difference between these two coalitional values is that the former is efficient, while the latter verifies a property of 2-efficiency.     

Development of a competitive lateral flow immunoassay for progesterone: influence of coating conjugates and buffer components

Several aspects of the development of competitive lateral flow immunoassays (LFIAs) are described. The quantitation of progesterone is taken as an example. The LFIA format consisted of a nitrocellulose membrane spotted with various progesterone conjugates as the test line. A mixture of primary antibody and secondary antibody adsorbed to colloidal carbon was used for signal generation. A digital scanner and dedicated software were used to quantitate the response. A reappraisal of the checkerboard titration, often used in the optimisation of immunoassays, is discussed. Surprisingly, the highest sensitivity of the LFIA format (IC₅₀ of 0.6 μg L⁻¹ progesterone in buffer) was achieved by using a high coating concentration of the analyte–protein conjugate and a high dilution of the antibody solution. Immediate addition of all reagents in LFIA was superior to premixing the components and allowing prereaction. Of several blocking agents tested bovine serum albumin was superior in performance, whereas the combination of ovalbumin and progesterone substantially influenced test results.     

HOW RAPID SHOULD EMISSION REDUCTION BE? A GAME‐THEORETIC APPROACH

Abstract In this paper, we search for multistage realization of international environmental agreements. To analyze countries' incentives and the results of their interactions, we mathematically represent players' strategic preferences and apply a game‐theoretic approach to make predictions about their outcomes. The initial decision on emissions reduction is determined by the Stackelberg equilibrium concept. We generalize Barrett's static “emission” model to a dynamic framework and answer the question “how rapid should the emission reduction be?” It appears that sharper abatement is desirable in the early term, which is similar to the conclusion of the Stern review. Numerical example demonstrates that abatement dynamics of the coalition and the free‐rider differ when discounting of the future payoffs increases. We show that without incentives from external organizations or governments, such pollution reduction path can actually lead to a decline in the agreement's membership size.     

On small blocking sets and their linearity

We prove that a small minimal blocking set of PG(2,q) is “very close” to be a linear blocking set over some subfield GF(pe)<GF(q). This implies that (i) a similar result holds in PG(n,q) for small minimal blocking sets with respect to k-dimensional subspaces (0?k?n) and (ii) most of the intervals in the interval-theorems of Sz?nyi and Sz?nyi-Weiner are empty.     

On the use of binary decision diagrams for solving problems on simple games

Simple games are yes/no cooperative games which arise in many practical applications. Recently, we have used reduced ordered binary decision diagrams and quasi-reduced ordered binary decision diagrams (abbreviated as Robdds and Qobdds, respectively) for the representation of simple games and for the computation of some power indices. In the present paper, we continue this work. We show how further important computational problems on simple games can be solved using Qobdds, viz. the identification of some key players, the computation of the desirability relation on individuals, the test whether a simple game is proper and strong, respectively, and the computation of Qobdd-representations for the sets of all minimal winning coalitions, all shift-minimal winning coalitions and all blocking coalitions, respectively. Applications of these solutions include the computation of recent power indices based on shift-minimal winning coalitions and the test for linear separability of a directed simple game.     

The effect of TiCl4-treated TiO2 compact layer on the performance of dye-sensitized solar cell

In order to prevent the charge recombination at the interface between the transparent-conducting oxide (TCO) substrate and electrolyte, a TiO₂ compact layer was deposited on the substrate by hydrolysis of TiCl₄ aqueous solution. Optimum thickness of the compact layer was found to be ∼25 nm, which showed ∼24% increase in the power-conversion efficiency compared with the bare cell. Impedance spectra indicated that the interfacial charge-transfer resistance of TCO/electrolyte interface was increased by more than a factor of three with the TiO₂ compact layer at 0.4 V. Moreover, the electron-carrier lifetime of the 25 nm-deposited cell was improved by a factor of five compared with the bare cell.     

Metropolis-Hastings Within Partially Collapsed Gibbs Samplers

The partially collapsed Gibbs (PCG) sampler offers a new strategy for improving the convergence of a Gibbs sampler. PCG achieves faster convergence by reducing the conditioning in some of the draws of its parent Gibbs sampler. Although this can significantly improve convergence, care must be taken to ensure that the stationary distribution is preserved. The conditional distributions sampled in a PCG sampler may be incompatible and permuting their order may upset the stationary distribution of the chain. Extra care must be taken when Metropolis-Hastings (MH) updates are used in some or all of the updates. Reducing the conditioning in an MH within Gibbs sampler can change the stationary distribution, even when the PCG sampler would work perfectly if MH were not used. In fact, a number of samplers of this sort that have been advocated in the literature do not actually have the target stationary distributions. In this article, we illustrate the challenges that may arise when using MH within a PCG sampler and develop a general strategy for using such updates while maintaining the desired stationary distribution. Theoretical arguments provide guidance when choosing between different MH within PCG sampling schemes. Finally, we illustrate the MH within PCG sampler and its computational advantage using several examples from our applied work.     

Influence of ferromagnetic layer on the exchange coupling of antiferromagnetic NiO-based films

Strong effects of ferromagnetic layer (FMCo, and Ni₈₀Fe₂₀) on the magnitude and blocking temperature of exchange coupling are observed in antiferromagnetic NiO-based films NiO (5 nm)/FM₁ (t nm)/FM₂ (6-t nm). The existence of interfacial spins configuration in glass-like state and FM anisotropy are proposed to interpret a minimum shown in thermal magnetization curves for films with strong exchange coupling effect. The microstructural change of FM layer and the long-range interaction of exchange bias are taken into account to explain a strong dependence of exchange coupling energy density on the thickness t_F of FM layer when t_F<5 nm.