We establish a representation of the core of convex measure games by means of rearrangement ideas and the notion of Kantorovich potentials. Our representation was first proved by Marinacci and Montrucchio [7] when the underlying measurable structure is that of a standard Borel space. The approach presented here is completely different and does not require this assumption.

Abstract We consider the constraints that can be imposed on a wide class of Inflation models in modified gravity scenarios in which the Friedmann equation is modified by the inclusion of ρ2 terms, where ρ is the total energy density. In particular we obtain the reheating temperature and gravitino abundance associated with the end of inflation. Whereas models of chaotic inflation and natural inf...

We use probabilistic techniques to study neural systems which improve the timing accuracy of action potential 'ring. A striking example of such accuracy was discovered in the columnar region of the VNLL by Covey and Casseday (J. Neurosci. 11 (1991) 3456). In response to sound stimulation, these VNLL cells 're an action potential whose latency under repeated trials has a standard deviation of ap...

The functions of biological macromolecules are inherently linked to their complex conformational behaviour. As a consequence of this complexity, the corresponding potential energy landscapes encompass multiple minima. Some of the intermediate structures between initial and final states can be characterized by experimental techniques. Computer simulations can explore the dynamics of individual s...

We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in terms of the Euclidean norm. For example, one can use the new approach to get separate error estimates for each action coordinate. An application...

Dissociation under ultrashort intense laser fields differs from the process occurring in the presence of a weak field by two main characteristics. In the strong field regime, the force exerted by the laser on the molecule is comparable to the intermolecular forces. In addition, this force is varying on a time scale comparable to that of the molecular vibration. The combination of these two effe...

Reliably decoding neuronal responses requires knowing what aspects of neuronal responses are stimulus related, and which aspects act as noise. Recent work shows that spike trains can be viewed as stochastic samples from the rate variation function, as estimated by the time dependent spike density function (or normalized peristimulus time histogram). Such spike trains are exactly described by or...