Psychometric functions for gap detection in noise measured from young and aged subjects.

Psychometric functions for gap detection of temporal gaps in wideband noise were measured in a "yes/no" paradigm from normal-hearing young and aged subjects with closely matched audiograms. The effects of noise-burst duration, gap location, and uncertainty of gap location were tested. A typical psychometric function obtained in this study featured a steep slope, which was independent of most experimental conditions as well as age. However, gap thresholds were generally improved with increasing duration of the noise burst for both young and aged subjects. Gap location and uncertainty had no significant effects on the thresholds for the young subjects. For the aged subjects, whenever the gap was sufficiently away from the onset or offset of the noise burst, detectability was robust despite uncertainty about the gap location. Significant differences between young and aged subjects could be observed only when the gap was very close to the signal onset and offset.     

Psychometric functions for level discrimination

To determine the form of psychometric functions for 2I,2AFC level discrimination (commonly called intensity discrimination), ten increment levels were presented in random order within blocks of 100 trials. Stimuli were chosen to encompass a wide range of conditions and difference limens: eight 10-ms tones had frequencies of 0.25, 1, 8, or 14 kHz and levels of 30, 60, or 90 dB SPL; two 500-ms stimuli also were tested: a 1-kHz tone at 90 dB SPL and broadband noise at 63 dB SPL. For each condition, at least 20 blocks were presented in mixed order. Results for five normal listeners show that the sensitivity, d', is nearly proportional to delta L (= 20 log [(p + delta p)/p], where p is sound pressure) over the entire range of difference limens. When d' is plotted against Weber fractions for sound pressure, delta p/p, or intensity, delta I/I, exponents of the best-fitting power functions decrease with increasing difference limens and are less than unity for large difference limens. The approximately proportional relation between d' and delta L agrees with modern multichannel models of level discrimination and with psychometric functions derived for single auditory-nerve fibers. The results also support the notion that the difference limen, expressed as delta LDL and plotted on a logarithmic scale, is an appropriate representation of performance in level-discrimination experiments.     

Psychometric functions for pure-tone frequency discrimination

The form of the psychometric function (PF) for auditory frequency discrimination is of theoretical interest and practical importance. In this study, PFs for pure-tone frequency discrimination were measured for several standard frequencies (200-8000 Hz) and levels [35-85 dB sound pressure level (SPL)] in normal-hearing listeners. The proportion-correct data were fitted using a cumulative-Gaussian function of the sensitivity index, d', computed as a power transformation of the frequency difference, Δf. The exponent of the power function corresponded to the slope of the PF on log(d')-log(Δf) coordinates. The influence of attentional lapses on PF-slope estimates was investigated. When attentional lapses were not taken into account, the estimated PF slopes on log(d')-log(Δf) coordinates were found to be significantly lower than 1, suggesting a nonlinear relationship between d' and Δf. However, when lapse rate was included as a free parameter in the fits, PF slopes were found not to differ significantly from 1, consistent with a linear relationship between d' and Δf. This was the case across the wide ranges of frequencies and levels tested in this study. Therefore, spectral and temporal models of frequency discrimination must account for a linear relationship between d' and Δf across a wide range of frequencies and levels.     

Psychometric functions for frequency discrimination from listeners with sensorineural hearing loss

Psychometric functions for pulsed pure-tone frequency discrimination were obtained from hearing-impaired listeners at frequencies with normal hearing and at frequencies with mild or moderate hearing losses. The general form of psychometric functions at hearing-impaired frequencies was found to be the same as at normal-hearing frequencies, i.e.,d' was linear with the frequency difference between tones, in Hz. For all but one psychometric function, the addition of an intercept term to the fitting equation did not account for significantly more variance than did the slope term alone. Therefore, it was concluded that psychometric functions for frequency discrimination can be adequately described with only one parameter: the slope of the psychometric function. Deficits in discrimination at hearing-loss frequencies were manifested by more gradual slopes of psychometric functions. Procedures for normalizing psychometric functions are presented, which facilitate comparisons of normal and impaired frequency discrimination data across studies and frequencies. Comparisons of dlf's (difference limen for frequency) obtained with adaptive and fixed procedures show a bias toward larger dlf's with adaptive procedures, but only at higher frequencies. A discussion of equal-interval and equal-ratio adaptive stepping rules indicates that an equal-ratio rule may be preferable.     

Truncation procedure for high order reduced distribution functions

The concept of the average force potentials is used to develop the truncation procedure for an arbitrary equation of the chain. The closed system of integral equations for the average force potentials is formulated. In the case when the truncation approximation involves the four-particle distribution function the expression for the configurational integral is derived. The internal energy and the pressure calculated in terms of the binary distribution function are thermodynamically compatible.     

Gap detection for similar and dissimilar gap markers

Detection thresholds for temporal gaps between markers of dissimilar frequency are usually elevated with respect to thresholds for gaps between markers of similar frequency. Because gaps between markers of dissimilar frequency represent both a spectrally based perceptual discontinuity as well as a temporal discontinuity, it is not clear what factors underlie the threshold elevation. This study sought to examine the effects of perceptual dissimilarities on gap detection. The first experiment measured gap detection for configurations of narrow-band gap markers comprised of pure tones, frequency-modulated tones, and amplitude-modulated tones. The results showed that gap thresholds for frequency-disparate pure-tone markers were elevated with respect to isofrequency tonal markers, but that perceptual discontinuities between markers restricted to the same frequency region did not uniformly elevate threshold. The second experiment measured gap detection for configurations of markers where the leading and trailing markers could differ along the dimensions of bandwidth, duration, and pitch. The results showed that, in most cases, gap detection deteriorated when the bandwidth of the two markers differed, even when the spectral content of the narrower-band marker was completely subsumed by the spectral content of the wider-band marker. This finding suggests that gap detection is sensitive to spectral dissimilarity between markers in addition to spectral discontinuity. The effects of marker duration depended on the marker bandwidth. Pitch differences across spectrally similar markers had no effect.     

Vibrotactile temporal gap detection as a function of age

The ability of subjects to detect temporal gaps between bursts of sinusoids or bursts of bandlimited noise was measured to evaluate the phenomenon of tactile "sensory persistence" in older persons. Vibratory stimuli were delivered to the right thenar eminence of 27 subjects ranging in age from 8-75 years. The subjects' task was to detect the presence of a silent interval or "gap" between flanking 350-ms vibrotactile stimuli. The gap-detection threshold, expressed as the amplitude of vibration relative to the absolute detection threshold, decreased as the gap duration increased and was higher for gaps in noise than for gaps in sinusoids. The threshold for detecting short gaps increased with age for noise stimuli, but not for sinusoidal stimuli. Furthermore, the gap-detection threshold recovered more rapidly in older subjects for noise stimuli, but less rapidly in older subjects for sinusoidal stimuli. Because of these differences, it appears that the effects of age on gap detection cannot be due to a simple increase in sensory persistence, but may be due to multiple processes.     

Mechanisms of modulation gap detection

It has been postulated that the central auditory system contains an array of modulation filters, each responsive to a different range of modulation frequencies present at the outputs of the (peripheral) auditory filters. In the present experiments, we tested what we call the "dip hypothesis," that a gap in modulation is detected using the "dip" in the output of the modulation filter tuned to the modulator frequency. In experiment 1, the task was to detect a gap in the sinusoidal amplitude modulation imposed on a 4-kHz carrier. The modulator preceding the gap ended with a positive-going zero-crossing. There were three conditions, differing in the phase at which the modulator started at the end of the gap; zero-phase, at a positive-going zero-crossing; pi-phase, at a negative-going zero-crossing; and "preserved" phase, at the phase the modulator would have had if it had continued without interruption. Modulation frequencies were 5, 10, 20, and 40 Hz. Psychometric functions for detection of the gap were measured using a two-alternative forced-choice task. For the zero-phase and preserved-phase conditions, the detectability index, d', increased monotonically with increasing gap duration. For the pi-phase condition, performance was good (d' > 1) for small gap durations, and initially worsened with increasing gap duration, before improving again for longer gap durations. This is the pattern of results expected from the dip hypothesis, provided that the modulation filters have Q values of 2 or more. However, it is also possible that a rhythm cue was used to improve performance in the pi-phase condition for short gap durations; the introduction of the gap markedly disrupted the regular rhythm produced by the modulator peaks. In experiment 2, the rhythm cue was disrupted by varying the modulator period randomly around its nominal value, except for the modulator periods immediately before and after the gap. This markedly impaired performance, and resulted in psychometric functions that were very similar for the zero-phase and pi-phase conditions. This pattern of results is inconsistent with the dip hypothesis. For both experiments, modulation gap "thresholds" (d' approximately 1) were roughly constant when expressed as a proportion of the modulator period. Possible mechanisms of modulation gap detection are discussed and evaluated.     

Modulation and gap detection for broadband and filtered noise signals

Modulation detection thresholds (as a function of sinusoidal amplitude modulation frequency) and temporal gap detection thresholds were measured for three low-pass-filtered noise signals (fc = 1000, 2000, and 4000 Hz), a high-pass-filtered noise signal (fc = 4000 Hz), and a broadband signal. The two latter noise signals were effectively low-pass filtered (fc = 6500 Hz) by the earphone. Each of the filtered signals was presented with a complementary filtered noise masker. Modulation and gap detection thresholds were lowest for the broadband and high-pass signals. Thresholds were significantly higher for the low-pass signals than for the broadband and high-pass signals. For these tasks and conditions, the high-frequency content of the noise signal was more important than was the signal bandwidth. Sensitivity (s) and time constant (tau) indices were derived from functions fitted to the modulation detection data. These indices were compared with gap detection thresholds for corresponding signals. The gap detection thresholds were correlated inversely (rho = -1.0, p less than 0.05) with s (i.e., smaller gap detection thresholds were correlated with greater sensitivity to modulation), but were not correlated significantly with tau, which was relatively invariant across signal conditions.     

A binaural analog of gap detection.

The temporal resolution of the binaural auditory system was measured using a binaural analog of gap detection. A binaural "gap" was defined as a burst of interaurally uncorrelated noise (Nu) placed between two bursts of interaurally correlated noise (N0). The Nu burst creates a dip in the output of a binaural temporal window integrating interaural correlation, analogous to the dip created by a silent gap in the output of a monaural temporal window integrating intensity. The equivalent rectangular duration (ERD) of the binaural window was used as an index of binaural temporal resolution. In order to derive the ERD, both the shortest-detectable binaural gap and the jnd for a reduction in interaural correlation from unity were measured. In experiment 1, binaural-gap thresholds were measured using narrow-band noise carriers as a function of center frequency from 250 to 2000 Hz (fixed 100-Hz bandwidth) and a function of lower-cutoff frequency from 100 to 400 Hz (fixed 500-Hz upper-cutoff frequency). Binaural-gap thresholds (1) increased significantly with increasing frequency in both tasks, and (2) at frequencies below 500 Hz, were shorter than corresponding silent-gap thresholds measured with the same N0 noises. In experiment 2, interaural-correlation jnd's were measured for the same conditions. The jnd's also increased significantly with increasing frequency. The results were analyzed using a temporal window integrating the output of a computational model of binaural processing. The ERD of the window varied widely across listeners, with a mean value of 140 ms, and did not significantly depend on frequency. This duration is about an order of magnitude longer than the ERD of the monaural temporal window and is, therefore, consistent with "binaural sluggishness."     

Within- and across-channel gap detection in cochlear implant listeners

This study examined within- and across-electrode-channel processing of temporal gaps in successful users of MED-EL COMBI 40+ cochlear implants. The first experiment tested across-ear gap duration discrimination (GDD) in four listeners with bilateral implants. The results demonstrated that across-ear GDD thresholds are elevated relative to monaural, within-electrode-channel thresholds; the size of the threshold shift was approximately the same as for monaural, across-electrode-channel configurations. Experiment 1 also demonstrated a decline in GDD performance for channel-asymmetric markers. The second experiment tested the effect of envelope fluctuation on gap detection (GD) for monaural markers carried on a single electrode channel. Results from five cochlear implant listeners indicated that envelopes associated with 50-Hz wide bands of noise resulted in poorer GD thresholds than envelopes associated with 300-Hz wide bands of noise. In both cases GD thresholds improved when envelope fluctuations were compressed by an exponent of 0.2. The results of both experiments parallel those found for acoustic hearing, therefore suggesting that temporal processing of gaps is largely limited by factors central to the cochlea.     

Independence of frequency channels in auditory temporal gap detection

The ability of listeners to detect a temporal gap in a 1600-Hz-wide noiseband (target) was studied as a function of the absence and presence of concurrent stimulation by a second 1600-Hz-wide noiseband (distractor) with a nonoverlapping spectrum. Gap detection thresholds for single noisebands centered on 1.0, 2.0, 4.0, and 5.0 kHz were in the range from 4 to 6 ms, and were comparable to those described in previous studies. Gap thresholds for the same target noisebands were only modestly improved by the presence of a synchronously gated gap in a second frequency band. Gap thresholds were unaffected by the presence of a continuous distractor that was either proximate or remote from the target frequency band. Gap thresholds for the target noiseband were elevated if the distractor noiseband also contained a gap which "roved" in time in temporal proximity to the target gap. This effect was most marked in inexperienced listeners. Between-channel gap thresholds, obtained using leading and trailing markers that differed in frequency, were high in all listeners, again consistent with previous findings. The data are discussed in terms of the levels of the auditory perceptual processing stream at which the listener can voluntarily access auditory events in distinct frequency channels.     

Psychometric functions for discrimination of two-component complex tones in listeners with normal hearing and listeners with hearing loss

This study compared the ability of 5 listeners with normal hearing and 12 listeners with moderate to moderately severe sensorineural hearing loss to discriminate complementary two-component complex tones (TCCTs). The TCCTs consist of two pure tone components (f1 and f2) which differ in frequency by delta f (Hz) and in level by delta L (dB). In one of the complementary tones, the level of the component f1 is greater than the level of component f2 by the increment delta L; in the other tone, the level of component f2 exceeds that of component f1 by delta L. Five stimulus conditions were included in this study: fc = 1000 Hz, delta L = 3 dB; fc = 1000 Hz, delta L = 1 dB; fc = 2000 Hz, delta L = 3 dB; fc = 2000 Hz, delta L = 1 dB; and fc = 4000 Hz, delta L = 3 dB. In listeners with normal hearing, discrimination of complementary TCCTs (with a fixed delta L and a variable delta f) is described by an inverted U-shaped psychometric function in which discrimination improves as delta f increases, is (nearly) perfect for a range of delta f's, and then decreases again as delta f increases. In contrast, group psychometric functions for listeners with hearing loss are shifted to the right such that above chance performance occurs at larger values of delta f than in listeners with normal hearing. Group psychometric functions for listeners with hearing loss do not show a decrease in performance at the largest values of delta f included in this study. Decreased TCCT discrimination is evident when listeners with hearing loss are compared to listeners with normal hearing at both equal SPLs and at equal sensation levels. In both groups of listeners, TCCT discrimination is significantly worse at high center frequencies. Results from normal-hearing listeners are generally consistent with a temporal model of TCCT discrimination. Listeners with hearing loss may have deficits in using phase locking in the TCCT discrimination task and so may rely more on place cues in TCCT discrimination.     

Relationships among age-related differences in gap detection and word recognition

The relationships among age-related differences in gap detection and word recognition in subjects with normal hearing or mild sensorineural hearing loss were explored in two studies. In the first study, gap thresholds were obtained for 40 younger and 40 older subjects. The gaps were carried by 150-ms, modulated, low-pass noise bursts with cutoff frequencies of 1 or 6 kHz. The noise bursts were presented at an overall level of 80 dB SPL in three background conditions. Mean gap thresholds ranged between 2.6 and 7.8 ms for the younger age group and between 3.4 and 10.0 ms for the older group. Mean gap thresholds were significantly larger for the older group in all six conditions. Gap thresholds were not significantly correlated with audiometric thresholds in either age group but the 1-kHz gap thresholds increased with age in the younger group. In the second study, the relationships among gap thresholds, spondee-in-babble thresholds, and audiometric thresholds of 66 subjects were examined. Compared with the older subjects, the younger group recognized the spondees at significantly lower (more difficult) spondee-to-babble ratios. In the younger group, spondee-in-babble thresholds were significantly correlated with gap thresholds in conditions of high-frequency masking. In the older group, spondee-in-babble thresholds, gap thresholds, and audiometric thresholds were not significantly correlated, but the spondee-in-babble thresholds and two audiometric thresholds increased significantly with age. These results demonstrate that significant age-related changes in auditory processing occur throughout adulthood. Specifically, age-related changes in temporal acuity may begin decades earlier than age-related changes in word recognition.     

Dynamical structure functions,collective modes,and energy gap in charged-particle bilayers

The dynamical properties of strongly coupled charged-particle bilayers are investigated by molecular dynamics (MD) simulation and theoretical analysis. The spectra of the current correlation functions show the existence of two (in-phase and out-of-phase) longitudinal and two (in-phase and out-of-phase) transverse collective modes. The out-of-phase modes possess finite frequencies at wave numbers k-->0, confirming the existence of the predicted long-wavelength energy gap in the bilayer system. A theoretical model based on an extended Feynman ansatz for the dynamical structure functions provides predictions on the strength of the collective modes that are verified by the MD experiment.     

Superconducting gap for a two-leg t-J ladder

Single-particle diagonal and off-diagonal Green's functions of a two-leg t-J ladder at 1/8 doping are investigated by exact diagonalizations techniques. A numerically tractable expression for the superconducting gap is proposed and the frequency dependence of the real and imaginary parts of the gap are determined. The role of the low-energy gapped spin modes, whose energies are computed by a (one-step) contractor renormalization procedure, is discussed.     

Bogoliubov transformation for a spatially varying gap

It is shown that a general Bogoliubov transformation can be used as an alternative to Gorkov's equations in studying the properties of superfluid ³He with a position-dependent gap matrix. Expressions are derived for the current density and the gradient free energy which are exact to first and second order, respectively, in the spatial inhomogeneity.     

Spectral integration and wideband analysis in gap detection and overshoot paradigms

Several listening conditions show that energy remote from a target frequency can deleteriously affect sensitivity. One interpretation of such results entails a wideband analysis involving a wide predetection filter. The present study tested the hypothesis that both temporal gap detection and overshoot results are consistent with a wideband analysis, as contrasted with statistical combination of information across independent channels. For gap detection, stimuli were random or comodulated 50-Hz-wide noise bands centered on 1000, 1932, 3569, and 6437 Hz. For overshoot, the masker was an 8-kHz low-pass filtered noise, with 5-ms tone bursts presented at the same center frequencies used for gap detection. Signals were presented with either 0- or 250-ms delay after masker onset. In each paradigm, the target was introduced at only one frequency or at all four frequencies. Results from gap detection conditions did not favor a wideband analysis interpretation: Results in the random condition were consistent with an optimal combination of cues across frequency. An across-channel interference effect was also evident when only one of the four bands contained the gap. Although results from the overshoot conditions were consistent with a wideband analysis interpretation, they were more parsimoniously accounted for in terms of statistical combination of information.