A mean-field approach to elastically coupled hair bundles.

We study the dynamics of oscillatory hair bundles which are coupled elastically in their deflection variable and are subject to noise. We present a stochastic description capturing the dynamics of the hair bundles' mean field. In particular, the presented derivation elucidates the origin of the previously described noise reduction by coupling. By comparison of simulations of the approximate dynamics and the full system, we verify our results. Furthermore, we demonstrate that the specific type of coupling considered implies coupling-induced changes in the dynamics beyond mere noise reduction.

The remarkable cochlear amplifier.

This composite article is intended to give the experts in the field of cochlear mechanics an opportunity to voice their personal opinion on the one mechanism they believe dominates cochlear amplification in mammals. A collection of these ideas are presented here for the auditory community and others interested in the cochlear amplifier. Each expert has given their own personal view on the topic and at the end of their commentary they have suggested several experiments that would be required for the decisive mechanism underlying the cochlear amplifier. These experiments are presently lacking but if successfully performed would have an enormous impact on our understanding of the cochlear amplifier.

Spontaneous movements and linear response of a noisy oscillator.

A deterministic system that operates in the vicinity of a Hopf bifurcation can be described by a single equation of a complex variable, called the normal form. Proximity to the bifurcation ensures that on the stable side of the bifurcation (i.e. on the side where a stable fixed point exists), the linear-response function of the system is peaked at the frequency that is characteristic of the oscillatory instability. Fluctuations, which are present in many systems, conceal the Hopf bifurcation and lead to noisy oscillations. Spontaneous hair bundle oscillations by sensory hair cells from the vertebrate ear provide an instructive example of such noisy oscillations. By starting from a simplified description of hair bundle motility based on two degrees of freedom, we discuss the interplay of nonlinearity and noise in the supercritical Hopf normal form. Specifically, we show here that the linear-response function obeys the same functional form as for the noiseless system on the stable side of the bifurcation but with effective, renormalized parameters. Moreover, we demonstrate in specific cases how to relate analytically the parameters of the normal form with added noise to effective parameters. The latter parameters can be measured experimentally in the power spectrum of spontaneous activity and linear-response function to external stimuli. In other cases, numerical solutions were used to determine the effects of noise and nonlinearities on these effective parameters. Finally, we relate our results to experimentally observed spontaneous hair bundle oscillations and responses to periodic stimuli.

Discretionary salt use in airline meal service.

Salt use in airline meal service was studied through observation of returned meal trays of 932 passengers. Observation and weighing of salt packets on returned trays revealed that 64% of passengers did not salt their airline dinner, while 6% used the entire salt packet, 0.92 gm NaCl (362 mg Na). Average discretionary salt use among the 234 passengers (25%) who added salt was 0.57 gm NaCl (232 mg Na). Estimates of total sodium in the four airline dinners averaged 2.0 gm NaCl (786 mg Na). Laboratory assays of menu items produced by the airline foodservice differed 3% to 19% from estimated values. Sodium content of the four airline dinner menus was similar and did not affect salt use. Discretionary salt use was related to the total amount of entrée consumed but was not affected by the amount of salad consumed. It is postulated that salt use in the "captive" airline situation is predicated on consistent, habitual practices. Lowering sodium consumption in this setting may require alteration in both food preparation methods and quantity of salt presented in the packets.