A computational algorithm for computing cochlear frequency selectivity: Further studies

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

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A computational algorithm for LU decomposition of a sequence of matrices that differ only in one or more elements

ACM SIGNUM Newsletter ◽

10.1145/74654.74656 ◽

1989 ◽

Vol 24 (4) ◽

pp. 8-16

Author(s):

M. S. Zahir

Keyword(s):

Computational Algorithm ◽

Lu Decomposition

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Subthreshold frequency selectivity in avian auditory thalamus

Journal of Neurophysiology ◽

10.1152/jn.1994.71.4.1361 ◽

1994 ◽

Vol 71 (4) ◽

pp. 1361-1372 ◽

Cited By ~ 12

Author(s):

B. Strohmann ◽

D. W. Schwarz ◽

E. Puil

Keyword(s):

Frequency Selectivity ◽

Membrane Properties ◽

Resting Potential ◽

Resonant Peak ◽

Auditory Signal ◽

Voltage Response ◽

Potential Range ◽

Na Current ◽

Frequency Responses ◽

Low Threshold

1. We studied the frequency responses of neurons in the nucleus ovoidalis (OV), the principal thalamic auditory relay nucleus of the chicken, in the subthreshold range of membrane potentials. The frequency response is the impedance amplitude profile evident in the voltage response to a broadband stimulus. The stimulus was a deterministic periodic current input of small amplitude, sweeping through a specified frequency range. We used whole-cell, tight-seal recording techniques in slices to study the voltage responses and membrane properties in current and voltage clamp. 2. Generally, low-frequency resonant humps with peak impedances of approximately 6 Hz characterized the frequency responses of OV neurons. This resonance was the principal determinant for frequency selectivity in the majority of OV neurons expressing only a tonic mode of firing. 3. The 6-Hz resonance was voltage dependent and most distinct where the activation ranges of a hyperpolarization activated inward current (IH) and a persistent Na+ current tend to overlap. The potential range for optimal resonance often included the resting potential. 4. Application of the Na+ current antagonist, tetrodotoxin, blocked the persistent Na+ current and most of the resonant hump at depolarized levels but did not affect the resonant peak along the frequency axis. Thus the persistent Na+ current may serve to amplify the resonance. 5. Extracellular application of Cs+, but not Ba2+, blocked a voltage sag during pulsed hyperpolarization as well as the IH current. Application of Cs+ also eliminated the 6-Hz resonance. An IH seems, therefore, instrumental for the resonance. 6. A minority of neurons that expressed low-threshold Ca2+ spikes and burst firing at hyperpolarized states displayed voltage oscillations at 2-4 Hz, spontaneously or in response to pulsatile stimuli. Application of Ni2+ blocked the oscillations and the low-threshold spikes, presumably produced by a T-type Ca2+ current. The resonance at 6 Hz, however, was only slightly affected by Ni2+. A T-type current, therefore, is critical for the 2- to 4-Hz oscillations. 7. Membrane resonance may dominate the power spectrum of subthreshold potential fluctuations. The resonance demonstrated in vitro may be stabilized by experimental procedures; its frequency may be different and more variable in vivo. Resonances in thalamic neurons may play a role in auditory signal processing in birds.

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The effects of contrast on visual orientation and spatial frequency discrimination: a comparison of single cells and behavior

Journal of Neurophysiology ◽

10.1152/jn.1987.57.3.773 ◽

1987 ◽

Vol 57 (3) ◽

pp. 773-786 ◽

Cited By ~ 186

Author(s):

B. C. Skottun ◽

A. Bradley ◽

G. Sclar ◽

I. Ohzawa ◽

R. D. Freeman

Keyword(s):

Spatial Frequency ◽

Striate Cortex ◽

Frequency Tuning ◽

Single Cells ◽

Frequency Discrimination ◽

Frequency Selectivity ◽

Response Amplitude ◽

Visual Orientation ◽

Characteristic Analysis ◽

Response Variance

We have compared the effects of contrast on human psychophysical orientation and spatial frequency discrimination thresholds and on the responses of individual neurons in the cat's striate cortex. Contrast has similar effects on orientation and spatial frequency discrimination: as contrast is increased above detection threshold, orientation and spatial frequency discrimination performance improves but reaches maximum levels at quite low contrasts. Further increases in contrast produce no further improvements in discrimination. We measured the effects of contrast on response amplitude, orientation and spatial frequency selectivity, and response variance of neurons in the cat's striate cortex. Orientation and spatial frequency selectivity vary little with contrast. Also, the ratio of response variance to response mean is unaffected by contrast. Although, in many cells, response amplitude increases approximately linearly with log contrast over most of the visible range, some cells show complete or partial saturation of response amplitude at medium contrasts. Therefore, some cells show a clear increase in slope of the orientation and spatial frequency tuning functions with increasing contrast, whereas in others the slopes reach maximum values at medium contrasts. Using receiver operating characteristic analysis, we estimated the minimum orientation and spatial frequency differences that can be signaled reliably as a response change by an individual cell. This analysis shows that, on average, the discrimination of orientation or spatial frequency improves with contrast at low contrasts more than at higher contrasts. Using the optimal stimulus for each cell, we estimated the contrast threshold of 48 neurons. Most cells had contrast thresholds below 5%. Thresholds were only slightly higher for nonoptimal stimuli. Therefore, increasing the contrast of sinusoidal gratings above approximately 10% will not produce large increases in the number of responding cells. The observed effects of contrast on the response characteristics of nonsaturating cortical cells do not appear consistent with the psychophysical results. Cells that reach their maximum response at low-to-medium contrasts may account for the contrast independence of psychophysical orientation and spatial frequency discrimination thresholds at medium and high contrasts.

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