Linear and nonlinear pathways of spectral information transmission in the cochlear nucleus

At the level of the cochlear nucleus (CN), the auditory pathway divides into several parallel circuits, each of which provides a different representation of the acoustic signal. Here, the representation of the power spectrum of an acoustic signal is analyzed for two CN principal cells—chopper neurons of the ventral CN and type IV neurons of the dorsal CN. The analysis is based on a weighting function model that relates the discharge rate of a neuron to first- and second-order transformations of the power spectrum. In chopper neurons, the transformation of spectral level into rate is a linear (i.e., first-order) or nearly linear function. This transformation is a predominantly excitatory process involving multiple frequency components, centered in a narrow frequency range about best frequency, that usually are processed independently of each other. In contrast, type IV neurons encode spectral information linearly only near threshold. At higher stimulus levels, these neurons are strongly inhibited by spectral notches, a behavior that cannot be explained by level transformations of first- or second-order. Type IV weighting functions reveal complex excitatory and inhibitory interactions that involve frequency components spanning a wider range than that seen in choppers. These findings suggest that chopper and type IV neurons form parallel pathways of spectral information transmission that are governed by two different mechanisms. Although choppers use a predominantly linear mechanism to transmit tonotopic representations of spectra, type IV neurons use highly nonlinear processes to signal the presence of wide-band spectral features.

Compression, gain, and nonlinear distortion in an active cochlear model with subpartitions

The propagation of inhomogeneous, weakly nonlinear waves is considered in a cochlear model having two degrees of freedom that represent the transverse motions of the tectorial and basilar membranes within the organ of Corti. It is assumed that nonlinearity arises from the saturation of outer hair cell active force generation. I use multiple scale asymptotics and treat nonlinearity as a correction to a linear hydroelastic wave. The resulting theory is used to explain experimentally observed features of the response of the cochlear partition to a pure tone, including: the amplification of the response in a healthy cochlea vs a dead one; the less than linear growth rate of the response to increasing sound pressure level; and the amount of distortion to be expected at high and low frequencies at basal and apical locations, respectively. I also show that the outer hair cell nonlinearity generates retrograde waves.

Comparison of parametric and nonparametric methods to map oligogenes by linkage

A sample of 95 sib pairs affected with insulin-dependent diabetes and typed with their normal parents for 28 markers on chromosome 6 has been analyzed by several methods. When appropriate parameters are efficiently estimated, a parametric model is equivalent to the β model, which is superior to nonparametric alternatives both in single point tests (as found previously) and in multipoint tests. Theory is given for meta-analysis combined with allelic association, and problems that may be associated with errors of map location and/or marker typing are identified. Reducing by multipoint analysis the number of association tests in a dense map can give a 3-fold reduction in the critical lod, and therefore in the cost of positional cloning.

The degree of nonlinearity and anisotropy of blood vessel elasticity

Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress–strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress–strain relationship derived from this function represents the sum of a linear stress–strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In the case of canine pulmonary artery in the arch region, Debes and Fung [Debes, J. C. & Fung, Y. C.(1995) Am. J. Physiol. 269, H433–H442] have shown that the linear regime of the stress–strain relationship extends from the zero-stress state to the homeostatic state and beyond. Both vessels, however, are anisotropic in both the linear and nonlinear regimes.

What is a linear process?

We argue that given even an infinitely long data sequence, it is impossible (with any test statistic) to distinguish perfectly between linear and nonlinear processes (including slightly noisy chaotic processes). Our approach is to consider the set of moving-average (linear) processes and study its closure under a suitable metric. We give the precise characterization of this closure, which is unexpectedly large, containing nonergodic processes, which are Poisson sums of independent and identically distributed copies of a stationary process. Proofs of these results will appear elsewhere.

Training and search methods for speech recognition.

Speech recognition involves three processes: extraction of acoustic indices from the speech signal, estimation of the probability that the observed index string was caused by a hypothesized utterance segment, and determination of the recognized utterance via a search among hypothesized alternatives. This paper is not concerned with the first process. Estimation of the probability of an index string involves a model of index production by any given utterance segment (e.g., a word). Hidden Markov models (HMMs) are used for this purpose [Makhoul, J. & Schwartz, R. (1995) Proc. Natl. Acad. Sci. USA 92, 9956-9963]. Their parameters are state transition probabilities and output probability distributions associated with the transitions. The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizer wishes to find the most probable utterance that could have caused the observed acoustic index string. That probability is the product of two factors: the probability that the utterance will produce the string and the probability that the speaker will wish to produce the utterance (the language model probability). Even if the vocabulary size is moderate, it is impossible to search for the utterance exhaustively. One practical algorithm is described [Viterbi, A. J. (1967) IEEE Trans. Inf. Theory IT-13, 260-267] that, given the index string, has a high likelihood of finding the most probable utterance.

Spectrum of 100-kyr glacial cycle: Orbital inclination, not eccentricity

Spectral analysis of climate data shows a strong narrow peak with period ≈100 kyr, attributed by the Milankovitch theory to changes in the eccentricity of the earth’s orbit. The narrowness of the peak does suggest an astronomical origin; however the shape of the peak is incompatible with both linear and nonlinear models that attribute the cycle to eccentricity or (equivalently) to the envelope of the precession. In contrast, the orbital inclination parameter gives a good match to both the spectrum and bispectrum of the climate data. Extraterrestrial accretion from meteoroids or interplanetary dust is proposed as a mechanism that could link inclination to climate, and experimental tests are described that could prove or disprove this hypothesis.