Nash equilibria in multi-agent motor interactions.

Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.

Detection of molecular interactions with modified ferrocene self-assembled monolayers.

Ferrocene-terminated self-assembled monolayers (Fc-SAMs) are one of the most studied molecular aggregates on metal electrodes. They are easy to fabricate and provide a stable and reproducible system to investigate the effect of the microenvironment on the electron transfer parameters. We propose a novel application for Fc-SAMs, the detection of molecular interactions, based on the modification of the SAM with target-specific receptors. Mixed SAMs were fabricated by coimmobilization on Au electrodes of thiolated alkane chains with three different head groups: hydroxy terminating head group, ferrocene head group, and a functional head group such as biotin. Upon binding, the intrinsic electric charge of the target (e.g., streptavidin) modifies the electrostatic potential at the plane of electron transfer, causing a shift in the formal potential E degrees '. The SAMs were characterized by AC voltammetry. The detection mechanism is confirmed by measurements of formal potential as a function of electrolyte pH.

Long-range interactions in turbulence and the energy decay problem.

We discuss the long-range interactions that arise in homogeneous turbulence as a consequence of the Biot-Savart law. We note that, somewhat surprisingly, these long-range correlations are very weak in decaying, isotropic turbulence, and we argue that this should also be true for magnetohydrodynamic, rotating and stratified turbulence. If this is indeed the case, it is possible to make explicit predictions for the rate of decay of energy in these anisotropic systems, and it turns out that these predictions are consistent with the available numerical and experimental evidence.