Quantum Prisoner’s Dilemma game on hypergraph networks

We study the possible advantages of adopting quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner’s Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three-player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.     

Infinitely repeated games of incomplete information: Symmetric case with random signals

We consider infinitely repeated two-person zero-sum games of incomplete information in which the signals are the same for both players and consist of probability distributions on a given alphabet. We show that such games have a value.     

Q-superlinear convergence of the iterates in primal-dual interior-point methods

Sufficient conditions are given for the Q-superlinear convergence of the iterates produced by primal-dual interior-point methods for linear complementarity problems. It is shown that those conditions are satisfied by several well known interior-point methods. In particular it is shown that the iteration sequences produced by the simplified predictor–corrector method of Gonzaga and Tapia, the simplified largest step method of Gonzaga and Bonnans, the LPF+ algorithm of Wright, the higher order methods of Wright and Zhang, Potra and Sheng, and Stoer, Wechs and Mizuno are Q-superlinearly convergent. Received: February 9, 2000 / Accepted: February 20, 2001?Published online May 3, 2001     

-injective rings and -stable primes

The notion of stability of the highest local cohomology module with respect to the Frobenius functor originates in the work of R. Hartshorne and R. Speiser. R. Fedder and K.-i. Watanabe examined this concept for isolated singularities by relating it to -rationality. The purpose of this note is to study what happens in the case of non-isolated singularities and to show how this stability concept encapsulates a few of the subtleties of tight closure theory. Our study can be seen as a generalization of the work by Fedder and Watanabe. We introduce two new ring invariants, the -stability number and the set of -stable primes. We associate to every ideal generated by a system of parameters and an ideal of multipliers denoted and obtain a family of ideals . The set is independent of and consists of finitely many prime ideals. It also equals prime ideal such that is -stable. The maximal height of such primes defines the -stability number.

     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

SiOx precipitate composition in Si,revisited: Discussion closed?

The composition SiO_x of oxide precipitates in Si has been discussed for the past thirty years with experimentally estimated x ‐values ranging between 1 and 2. It is shown that this spread of x ‐values can be explained by calculating the average composition taking into account temperature and anneal time dependent size and shape of the precipitates and the limitations and probing volumes of the various characterization techniques. Hereby it is assumed that the oxygen‐rich (SiO₂?) core of the precipitates is surrounded by a 2 nm thin SiO layer as revealed by recent electron energy loss spectroscopy analyses. For plate‐like precipitates thinner than and for octahedral precipitates smaller than 6 nm, x ≈ 1. For larger precipitates, the central part of the precipitate consists of SiO_x with x close to 2 and the precipitate has an average x between 1 and 1.3 for plate‐like and up to 1.9 for octahedral precipitates. The predicted x ‐values for different precipitate sizes and morphologies, are compared with published experimental data. SiO_x precipitate nucleation and initial growth should be simulated assuming x = 1 and Fourier transform infrared spectra of precipitates assuming a mixture of SiO₂ and amorphous Si. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Fluorescence Properties of Selected Benzo[c]phenanthridines

The fluorescence properties of selected benzo[c]phenanthridines (BPs) were examined. The effect of structure, pH and solvent on the fluorescence properties has been investigated. It was found out that the presence of charged iminium nitrogen significantly decreased the fluorescence of the compounds. The fluorescence (intensity as well as emission spectra shape) of the investigated compounds was significantly dependent on pH as well as used solvent. The utilization in epigenetic modification mechanisms studies as demethylase probe and as possible pH indicator was suggested.     

Bounding the distance among longest paths in a connected graph

It is easy to see that in a connected graph any $2$ longest paths have a vertex in common. For $k\ge 7$, Skupień in 1966 obtained a connected graph in which some $k$ longest paths have no common vertex, but every $k?1$ longest paths have a common vertex. It is not known whether every $3$ longest paths in a connected graph have a common vertex and similarly for 4, 5, and $6$ longest path. Fujita et al. in 2015 give an upper bound on distance among $3$ longest paths in a connected graph. In this paper we give a similar upper bound on distance between $4$ longest paths and also for $k$ longest paths, in general.