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An algorithm is presented to adapt the coefficients of an array of FIR filters, whose outputs are linearly coupled to another array of error detection points, so that the sum of all the mean square error signals is minimized. The algorithm uses the instantaneous gradient of the total error, and for a single filter and error reduces to the "filtered x LMS" algorithm. The application of this algorithm to active sound and vibration control is discussed, by which suitably driven secondary sources are used to reduce the levels of acoustic or vibrational fields by minimizing the sum of the squares of a number of error sensor signals. A practical implementation of the algorithm is presented for the active control of sound at a single frequency. The algorithm converges on a timescale comparable to the response time of the system to be controlled, and is found to be very robust. If the pure tone reference signal is synchronously sampled, it is found that the behavior of the adaptive system can be completely described by a matrix of linear, time invariant, transfer functions. This is used to explain the behavior observed in simulations of a simplified single input, single output adaptive system, which retains many of the properties of the multichannel algorithm.

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Two formulations for calculating the total acoustic power radiated by a structure are compared; in terms of the amplitudes of the structural modes and in terms of the velocities of an array of elemental radiators on the surface of the structure. In both cases, the sound radiation due to the vibration of one structural mode or element is dependent on the vibration of other structural modes or elements. Either of these formulations can be used to describe the sound power radiation in terms of a set of velocity distributions on the structure whose sound power radiation is independent of the amplitudes of the other velocity distributions. These velocity distributions are termed "radiation modes." Examples of the shapes and radiation efficiencies of these radiation modes are discussed in the cases of a baffled beam and a baffled panel. The implications of this formulation for the active control of sound radiation from structures are discussed. In particular, the radiation mode formulation can be used to provide an estimate of the number of independent parameters of the structural response which need to be measured and controlled to give a required attenuation of the radiated sound power.

The stability of a linear model of the active cochlea is difficult to determine from its calculated frequency response alone. A state space model of the cochlea is presented, which includes a discretized set of general micromechanical elements coupled via the cochlear fluid. The stability of this time domain model can be easily determined in the linear case, and the same framework used to simulate the time domain response of nonlinear models. Examples of stable and unstable behavior are illustrated using the active micromechanical model of Neely and Kim. The stability of this active cochlea is extremely sensitive to abrupt spatial inhomogeneities, while smoother inhomogeneities are less likely to cause instability. The model is a convenient tool for investigating the presence of instabilities due to random spatial inhomogeneities. The number of unstable poles is found to rise sharply with the relative amplitude of the inhomogeneities up to a few percent, but to be significantly reduced if the spatial variation is smoothed. In a saturating nonlinear model, such instabilities generate limit cycles that are thought to produce spontaneous otoacoustic emissions. An illustrative time domain simulation is presented, which shows how an unstable model evolves into a limit cycle, distributed along the cochlea.

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In the present study, we investigated the function and the mechanism of action of RGS3, a member of a family of proteins called regulators of G protein signaling (RGS). Polyclonal antibodies against RGS3 were produced and characterized. An 80-kDa protein was identified as RGS3 by immunoprecipitation and immunoblotting with anti-RGS3 antibodies in a human mesangial cell line (HMC) stably transfected with RGS3 cDNA. Coimmunoprecipitation experiments in RGS3-overexpressing cell lysates revealed that RGS3 bound to aluminum fluoride-activated Galpha11 and to a lesser extent to Galphai3 and that this binding was mediated by the RGS domain of RGS3. A role of RGS3 in postreceptor signaling was demonstrated by decreased calcium responses and mitogen-activated protein (MAP) kinase activity induced by endothelin-1 in HMC stably overexpressing RGS3. Moreover, depletion of endogenous RGS3 by transfection of antisense RGS3 cDNA in NIH 3T3 cells resulted in enhanced MAP kinase activation induced by endothelin-1. The study of intracellular distribution of RGS3 indicated its unique cytosolic localization. Activation of G proteins by AlF4-, NaF, or endothelin-1 resulted in redistribution of RGS3 from cytosol to the plasma membrane as determined by Western blotting of the cytosolic and particulate fractions with RGS3 antiserum as well as by immunofluorescence microscopy. Agonist-induced translocation of RGS3 occurred by a dual mechanism involving both C-terminal (RGS domain) and N-terminal regions of RGS3. Thus, coexpression of RGS3 with a constitutively active mutant of Galpha11 (Galpha11-QL) resulted in the binding of RGS3, but not of its N-terminal fragment, to the membrane fraction and in its interaction with Galpha11-QL in vitro without any stimuli. However, both full-length RGS3 and its N-terminal domain translocated to the plasma membrane upon stimulation of intact cells with endothelin-1 as assayed by immunofluorescence microscopy. The effect of endothelin-1 was also mimicked by calcium ionophore A23187, suggesting the importance of Ca2+ in the mechanism of redistribution of RGS3. These data indicate that RGS3 inhibits G protein-coupled receptor signaling by a complex mechanism involving its translocation to the membrane in addition to its established function as a GTPase-activating protein.