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.

Motor coordination: when two have to act as one.

Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as "choosing sides," "stag hunt," "chicken," and "battle of sexes". In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players' movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players' responses. Moreover, we found that the probability of successful coordination depends on the players' initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

Building the perfect 3D hologram

A new liquid crystal device structure has been developed using a vertically grown Multi-Wall Carbon NanoTube (MWCNT) as a 3D electrode structure, which allows complicated phase only hologram to be displayed using conventional liquid crystal materials. The nanotubes act as an individual electrode sites that generate an electric field profile, dictating the refractive index profile with the liquid crystal cell. Changing the electric field applied makes it possible to tune the properties to modulate the light in an ideal kinoform. A perfect 3D image can be generated by a computer generated hologram by using the diffraction of the light from the hologram pixels to create an optical wave front that appears to come from 3D object. A multilevel phase modulating device based on nematic LC's is also under progress, which will be used with the LC/CNT devices on an LCOS backplane to project a full 3D image from the kinoform.

Is the assumption of perfect channel-state information in fading channels a good assumption?

Fading channels, which are used as a model for wireless communication, are often analyzed by assuming that the receiver is aware of the realization of the channel. This is commonly justified by saying that the channel varies typically slowly with time, and the receiver is thus able to estimate it. However, this assumption is optimistic, since it is prima facie not clear whether the channel can be estimated perfectly. This paper investigates the quality of this assumption by means of the channel capacity. In particular, results on the channel capacity of fading channels are presented, both when the receiver is aware of the realization of the channel and when it is aware only of its statistics. A comparison of these results demonstrates that information- theoretic analyses of fading channels that are based on the assumption that the receiver is aware of the channel's realization can yield helpful insights, but have to be taken with a pinch of salt. ©2009 IEEE.

On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria

This paper presents proof-certificate based sufficient conditions for the existence of Zeno behavior in hybrid systems near non-isolated Zeno equilibria. To establish these conditions, we first prove sufficient conditions for Zeno behavior in a special class of hybrid systems termed first quadrant interval hybrid systems. The proof-certificate sufficient conditions are then obtained through a collection of functions that effectively "reduce" a general hybrid system to a first quadrant interval hybrid system. This paper concludes with an application of these ideas to Lagrangian hybrid systems, resulting in easily verifiable sufficient conditions for Zeno behavior. © 2008 IEEE.