On the existence of Nash equilibria in large games

We study the existence of Nash equilibria in games with an infinite number of players. We show that there exists a Nash equilibrium in mixed strategies in all normal form games such that pure strategy sets are compact metric spaces and utility functions are continuous. The player set can be any nonempty set.     

Characteristics of multivariate distributions and the invariant coordinate system

We consider a semiparametric multivariate location–scatter model where the standardized random vector of the model is fixed using simultaneously two location vectors and two scatter matrices. The approach using location and scatter functionals based on the first four moments serves as our main example. The four functionals yield in a natural way the corresponding skewness, kurtosis and unmixing matrix functionals. Affine transformation based on the unmixing matrix transforms the variable to an invariant coordinate system. The limiting properties of the skewness, kurtosis, and unmixing matrix estimates are derived under general conditions. We discuss related statistical inference problems, the role of the sample statistics in testing for normality and ellipticity, and connections to invariant coordinate selection and independent component analysis.     

Synthesis and Structural, Magnetic and EPR Characterization of Discrete Finite Antiferromagnetic Chains

The synthesis, magnetic and electron paramagnetic resonance (EPR) characterisation of isolated, discrete, {Cr _n ^III } antiferromagnetically coupled chain complexes is reported for n = 6 and 7. Previous studies had reported supramolecular linked {Cr _n ^III } _x species. For n = 6, the lowest lying total spin state is diamagnetic with S = 1 and 2 first and second excited states, respectively; for n = 7, the lowest lying total spin state is S = 3/2 with S = 1/2 and 5/2 first and second excited states, respectively. The zero-field splittings of these states are well defined by low-temperature, multi-frequency EPR spectroscopy.     

A Novel Intramolecular Cyclization Reaction: Facile Solvent-Free Microscale Synthesis Suitable for Rapid Production of Libraries of 3-Amino-1,2,4-Triazines and for Combinatorial Chemistry

A novel intramolecular cyclization reaction is reported, in which various 1,2-bis(amidinohydrazone)s are converted into 3-amino-1,2,4-triazine or its substituted analogues. The reaction is easily carried out at microscale as well as ordinary scale level by heating the appropriate bis(amidinohydrazone) to roughly 200°C in an inert atmosphere or in vacuo. No solvents or other reagents are needed. The products are easily isolated, being sublimed off from the starting material and forming single crystals. A microscale procedure employing glass ampoules as the reaction vessel is described. The reaction is rapid and offers a facile way of preparing large series of substituted 3-amino-1,2,4-triazines individually in crystalline form for screening purposes. Because large numbers of bis(amidinohydrazone)s have been synthesized for biochemistry and drug development and libraries exist, the present method may be more practical than combinatorial approaches for the production of 3-amino-1,2,4-triazines, as it allows simultaneous individual syntheses. As the reaction is intramolecular, it is probable that the method can also be used also for mixtures of bis(amidinohydrazone)s to produce several triazines in one ampoule. The structure of the products was confirmed by mass, NMR and IR spectroscopy, elemental analyses and comparison with authentic samples. The reaction was studied using five bis(amidinohydrazone)s of aliphatic glyoxals, phenylglyoxal bis(amidinohydrazone) as well as the bis(amidinohydrazone) of 1,2-cyclohexanedione as starting materials. From the compound mentioned last a bicyclic product was obtained. In the case of the unsymmetric starting material ethylglyoxal bis(amidinohydrazone), both possible isomers were formed. The safety of heating the nitrogen-rich starting materials in large-scale syntheses has not been verified.     

Disentangling the effects of phonation and articulation: Hemispheric asymmetries in the auditory N1m response of the human brain

Background  

The cortical activity underlying the perception of vowel identity has typically been addressed by manipulating the first and second formant frequency (F1 & F2) of the speech stimuli. These two values, originating from articulation, are already sufficient for the phonetic characterization of vowel category. In the present study, we investigated how the spectral cues caused by articulation are reflected in cortical speech processing when combined with phonation, the other major part of speech production manifested as the fundamental frequency (F0) and its harmonic integer multiples. To study the combined effects of articulation and phonation we presented vowels with either high (/a/) or low (/u/) formant frequencies which were driven by three different types of excitation: a natural periodic pulseform reflecting the vibration of the vocal folds, an aperiodic noise excitation, or a tonal waveform. The auditory N1m response was recorded with whole-head magnetoencephalography (MEG) from ten human subjects in order to resolve whether brain events reflecting articulation and phonation are specific to the left or right hemisphere of the human brain.     

Direct determination of the anisotropy and exchange splittings in the dimeric single-molecule magnet [Mn4O3Cl4(O2CEt)3(py)3]2.8MeCN by inelastic neutron scattering

Energy splittings resulting from anisotropy and exchange interactions in the dimer of single-molecule magnets [Mn4O3Cl4(O2CEt)3(py)3]2.8MeCN are determined for both an undeuterated and a partially deuterated sample using inelastic neutron scattering. The antiferromagnetic (AF) exchange coupling between the two Mn4 subunits strongly depends on their separation. The Cl...Cl distance between the two subunits can be modified either by exchanging the solvent of crystallization or by deuteration of the C-H...Cl hydrogen bonds. The exchange of acetonitrile for n-hexane leads to a five times greater shortening of the Cl...Cl separation than does full deuteration of all the hydrogen bonds. As a result, the AF exchange coupling constants between the subunits are 0.0073(4) and 0.0103(9) meV in the samples with acetonitrile and n-hexane solvent molecules, respectively, in the crystal structure. On the other hand, the effect of C-H...Cl deuteration on the AF exchange coupling is not detectable within the experimental accuracy of INS.     

Catalytic CO oxidation by free Au2-: experiment and theory

Temperature-dependent rf-ion trap mass spectrometry and first-principles simulations reveal the detailed reaction mechanism of the catalytic gas-phase oxidation of CO by free Au(2)(-) ions in the presence of O(2). A metastable intermediate with a mass of Au(2)CO(3)(-) was observed at low temperatures. Two alternative structures corresponding to digold carbonate or peroxyformate are predicted for this intermediate. Both structures are characterized by low activation barriers for the formation of CO(2). These combined experimental and theoretical investigations provide a comprehensive understanding of the kinetics, energetics, and atomic arrangements along the reaction path, thus allowing a formulation of the catalytic cycle for the oxidation reaction.     

A fuzzy solution to a majority voting game

In the Fiorina-Plott majority voting game experiment several puzzling phenomena were discovered: (1) In the experiment series where the payoffs were small in general, the predictive performance of the core was markedly worse than in the high payoff series. (2) The core outcome was found to be defeatable by another proposal. (3) Some of the majority winning social outcomes were Pareto-suboptimal. (4) Even when there was no theoretical equilibrium point, there was a clear clustering of outcomes. The paper outlines a fuzzy decision making procedure which seems to be capable of explaining all the puzzling features (1)–(4). In the absence of data on membership functions the explanation provided is of non-predictive nature; it renders the observed outcomes plausible without precisely predicting each one of them.     

Negative gastrointestinal contrast enhancement and image distortion induced by superparamagnetic particles at 0.02 Tesla

Gastrointestinal contrast enhancement and image distortion induced by superparamagnetic particles were evaluated in vitro and in rabbits at 0.02 Tesla. Test tubes containing 0.01–1.0 mg particles/ml were imaged in an oil or water bath in order to demonstrate the concentration-dependent signal void and image distortion in vitro at several pulse sequences. The lowest concentration of particles tested clearly decreased the signal intensity. Image distortion was observed when the concentration exceeded 0.07 mg/ml and was more pronounced on the T₂-weighted images. The in vitro T₂ relaxation time decreased from 122 ms to 56 ms with an increase in the particle concentration from 0.01 to 0.06 mg/ml. A loss of the GI-tract signal was observed in rabbits after the administration of 1 mg particles/kg, given as a 0.03 mg/ml suspension. At a dose of 20 mg/kg (0.6 mg/ml suspension) significant image distortion was observed.     

Approaches to collective decision making with fuzzy preference relations

Recent experimental studies show that the predictive accuracy of many of the solution concepts derived from the collective decision making theory leaves much to be desired. In a previous paper the author attempted to explain some of the inaccuracies in terms of the fuzzy indifference regions of the individuals participating in the voting game. This paper gives straightforward generalizations of the solutions concepts in terms of the fuzzy social or individual preference relations. It turns out that some of these new solution concepts cotain their nonfuzzy counterparts as subsets. Others, in turn, are subsets of their nonfuzzy counterparts. We also discuss a method of aggregating individual nonfuzzy preferences so as to get a fuzzy social preference relation and, furthermore, a nonfuzzy social choice set.