A multiplicative potential approach to solutions for cooperative TU-games

Concerning the solution theory for cooperative games with transferable utility, it is well-known that the Shapley value is the most appealing representative of the family of (not necessarily efficient) game-theoretic solutions with an additive potential representation. This paper introduces a new solution concept, called Multiplicativily Proportional ($MP$) value, that can be regarded as the counterpart of the Shapley value if the additive potential approach to the solution theory is replaced by a multiplicative potential approach in that the difference of two potential evaluations is replaced by its quotient. One out of two main equivalence theorems states that every solution with a multiplicative potential representation is equivalent to this specifically chosen efficient value in that the solution of the initial game coincides with the $MP$ value of an auxiliary game. The associated potential function turns out to be of a multiplicative form (instead of an additive form) with reference to the worth of all the coalitions. The second equivalence theorem presents four additional characterizations of solutions that admit a multiplicative potential representation, e.g., preservation of discrete ratios or path independence

Kinetic approach to the cluster liquid-gas transition

The liquid-gas transition in free atomic clusters is investigated theoretically based on simple unimolecular rate theories and assuming sequential evaporations. A kinetic Monte Carlo scheme is used to compute the time-dependent properties of clusters undergoing multiple dissociations, and two possible definitions of the boiling point are proposed, relying on the cluster or gas temperature. This numerical approach is supported by molecular dynamics simulations of clusters made of sodium atoms or C60 molecules, as well as simplified rate equation

Fuzzy Control of Chaos

We introduce the idea of the fuzzy control of chaos: we show how fuzzy logic can be applied to the control of chaos, and provide an example of fuzzy control used to control chaos in Chua's circuit

Antiferromagnetic spin chain behavior and a transition to 3D magnetic order in Cu(D,L-alanine)2: Roles of H-bonds

We study the spin chain behavior, a transition to 3D magnetic order and the magnitudes of the exchange interactions for the metal-amino acid complex Cu(D,L-alanine)2.H2O, a model compound to investigate exchange couplings supported by chemical paths characteristic of biomolecules. Thermal and magnetic data were obtained as a function of temperature (T) and magnetic field (B0). The magnetic contribution to the specific heat, measured between 0.48 and 30 K, displays above 1.8 K a 1D spin-chain behavior that can be fitted with an intrachain antiferromagnetic (AFM) exchange coupling constant 2J0 = (-2.12 $\pm$ 0.08) cm$^{-1}$, between neighbor coppers at 4.49 {\AA} along chains connected by non-covalent and H-bonds. We also observe a narrow specific heat peak at 0.89 K indicating a phase transition to a 3D magnetically ordered phase. Magnetization curves at fixed T = 2, 4 and 7 K with B0 between 0 and 9 T, and at T between 2 and 300 K with several fixed values of B0 were globally fitted by an intrachain AFM exchange coupling constant 2J0 = (-2.27 $\pm$ 0.02) cm$^{-1}$ and g = 2.091 $\pm$ 0.005. Interchain interactions J1 between coppers in neighbor chains connected through long chemical paths with total length of 9.51 {\AA} are estimated within the range 0.1 < |2J1| < 0.4 cm$^{-1}$, covering the predictions of various approximations. We analyze the magnitudes of 2J0 and 2J1 in terms of the structure of the corresponding chemical paths. The main contribution in supporting the intrachain interaction is assigned to H-bonds while the interchain interactions are supported by paths containing H-bonds and carboxylate bridges, with the role of the H-bonds being predominant. We compare the obtained intrachain coupling with studies of compounds showing similar behavior and discuss the validity of the approximations allowing to calculate the interchain interactions.Comment: 10 pages, 4 figure

Electrochemical Studies of Redox Systems for Energy Storage

Particular attention was paid to the Cr(II)/Cr(III) redox couple in aqueous solutions in the presence of Cl(-) ions. The aim of this research has been to unravel the electrode kinetics of this redox couple and the effect of Cl(1) and electrode substrate. Gold and silver were studied as electrodes and the results show distinctive differences; this is probably due to the role Cl(-) ion may play as a mediator in the reaction and the difference in state of electrical charge on these two metals (difference in the potential of zero charge, pzc). The competition of hydrogen evolution with CrCl3 reduction on these surfaces was studied by means of the rotating ring disk electrode (RRDE). The ring downstream measures the flux of chromous ions from the disk and therefore separation of both Cr(III) and H2 generation can be achieved by analyzing ring and disk currents. The conditions for the quantitative detection of Cr(2+) at the ring electrode were established. Underpotential deposition of Pb on Ag and its effect on the electrokinetics of Cr(II)/Cr(III) reaction was studied

“Some like it hot”:spectators who score high on the personality trait openness enjoy the excitement of hearing dancers breathing without music

Music is an integral part of dance. Over the last 10 years, however, dance stimuli (without music) have been repeatedly used to study action observation processes, increasing our understanding of the influence of observer’s physical abilities on action perception. Moreover, beyond trained skills and empathy traits, very little has been investigated on how other observer or spectators’ properties modulate action observation and action preference. Since strong correlations have been shown between music and personality traits, here we aim to investigate how personality traits shape the appreciation of dance when this is presented with three different music/sounds. Therefore, we investigated the relationship between personality traits and the subjective esthetic experience of 52 spectators watching a 24 min lasting contemporary dance performance projected on a big screen containing three movement phrases performed to three different sound scores: classical music (i.e., Bach), an electronic sound-score, and a section without music but where the breathing of the performers was audible. We found that first, spectators rated the experience of watching dance without music significantly different from with music. Second, we found that the higher spectators scored on the Big Five personality factor openness, the more they liked the no-music section. Third, spectators’ physical experience with dance was not linked to their appreciation but was significantly related to high average extravert scores. For the first time, we showed that spectators’ reported entrainment to watching dance movements without music is strongly related to their personality and thus may need to be considered when using dance as a means to investigate action observation processes and esthetic preferences

Three-frequency resonances in dynamical systems

We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental device (an electronic oscillator). We compare the hierarchies of three-frequency resonances we find in each of these systems. All three show similar qualitative behaviour, suggesting the existence of generic features in the parameter-space organization of three-frequency resonances.Comment: See home page http://lec.ugr.es/~julya

Composition-induced structural transitions in mixed rare-gas clusters

The low-energy structures of mixed Ar--Xe and Kr--Xe Lennard-Jones clusters are investigated using a newly developed parallel Monte Carlo minimization algorithm with specific exchange moves between particles or trajectories. Tests on the 13- and 19- atom clusters show a significant improvement over the conventional basin-hopping method, the average search length being reduced by more than one order of magnitude. The method is applied to the more difficult case of the 38-atom cluster, for which the homogeneous clusters have a truncated octahedral shape. It is found that alloys of dissimilar elements (Ar--Xe) favor polytetrahedral geometries over octahedra due to the reduced strain penalty. Conversely, octahedra are even more stable in Kr--Xe alloys than in Kr_38 or Xe_38, and they show a core-surface phase separation behavior. These trends are indeed also observed and further analysed on the 55-atom cluster. Finally, we correlate the relative stability of cubic structures in these clusters to the glassforming character of the bulk mixtures.Comment: 14 pages, 8 figures, 5 tables PRB vol 70, in pres