We present a CCD photometric survey of the central one-half degree of the old open cluster, M67, in U, B, V, and I colors to magnitude V=20. Extensive comparison of our photometry with other published datasets shows excellent agreement, indicating that CCD photometry is capable of producing a uniform set of measurements consistent with the photometric system defined primarily by the Landolt standard sequence. The color-magnitude diagram of the cluster shows a well-defined main sequence extending at least to the limit of the photometry at Mv=10.55 and a substantial binary sequence. At least 38% of cluster stars are binaries. The current generation of theoretical isochrones cannot be fit to the observed sequences with the observational errors. We find a tendency for more massive members of the cluster to be more centrally concentrated, along with a turnover in the cluster luminosity function at low masses, which may be due to dynamical relaxation of the cluster. To the limit of our photometry, we find a mass of the cluster of 724 solar masses. In addition, we present a sample of stars of well-determined standard magnitudes that are suitable as photometric standards for further studies of this cluster and for general calibration of UBVI photometry using CCDs.

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A mathematical model describing the coupling between two independent amplification mechanisms in auditory hair cells is proposed and analyzed. Hair cells are cells in the inner ear responsible for translating sound-induced mechanical stimuli into an electrical signal that can then be recorded by the auditory nerve. In nonmammals, two separate mechanisms have been postulated to contribute to the amplification and tuning properties of the hair cells. Models of each of these mechanisms have been shown to be poised near a Hopf bifurcation. Through a weakly nonlinear analysis that assumes weak periodic forcing, weak damping, and weak coupling, the physiologically based models of the two mechanisms are reduced to a system of two coupled amplitude equations describing the resonant response. The predictions that follow from an analysis of the reduced equations, as well as performance benefits due to the coupling of the two mechanisms, are discussed and compared with published experimental auditory nerve data.

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