Function Of Interval Size Research Articles

Model selection for identifying power-law scaling

Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present.

Accuracy of Cochlear Implant Recipients on Pitch Perception, Melody Recognition, and Speech Reception in Noise

The purposes of this study were to (a) examine the accuracy of cochlear implant recipients who use different types of devices and signal processing strategies on pitch ranking as a function of size of interval and frequency range and (b) to examine the relations between this pitch perception measure and demographic variables, melody recognition, and speech reception in background noise. One hundred fourteen cochlear implant users and 21 normal-hearing adults were tested on a pitch discrimination task (pitch ranking) that required them to determine direction of pitch change as a function of base frequency and interval size. Three groups were tested: (a) long electrode cochlear implant users (N = 101); (b) short electrode users that received acoustic plus electrical stimulation (A+E) (N = 13); and (c) a normal-hearing (NH) comparison group (N = 21). Pitch ranking was tested at standard frequencies of 131 to 1048 Hz, and the size of the pitch-change intervals ranged from 1 to 4 semitones. A generalized linear mixed model (GLMM) was fit to predict pitch ranking and to determine if group differences exist as a function of base frequency and interval size. Overall significance effects were measured with Chi-square tests and individual effects were measured with t-tests. Pitch ranking accuracy was correlated with demographic measures (age at time of testing, length of profound deafness, months of implant use), frequency difference limens, familiar melody recognition, and two measures of speech reception in noise. The long electrode recipients performed significantly poorer on pitch discrimination than the NH and A+E group. The A+E users performed similarly to the NH listeners as a function of interval size in the lower base frequency range, but their pitch discrimination scores deteriorated slightly in the higher frequency range. The long electrode recipients, although less accurate than participants in the NH and A+E groups, tended to perform with greater accuracy within the higher frequency range. There were statistically significant correlations between pitch ranking and familiar melody recognition as well as with pure-tone frequency difference limens at 200 and 400 Hz. Low-frequency acoustic hearing improves pitch discrimination as compared with traditional, electric-only cochlear implants. These findings have implications for musical tasks such as familiar melody recognition.

A test of the Pfanzagl bisection model in rats.

The bisection method of animal psychophysical scaling was examined as a measurement procedure. The critical assumptions of bisection scaling, as described by Pfanzagl (1968), were tested to determine if a valid equal-interval scale could be derived. A valid scale was derived in which subjective time for the rat was a power function of real time. Bisection points were found to be context dependent, because the spacing of stimuli significantly affected the bisection points. Such context effects were directly related to the size of the interval bisected, whereas measurement errors in estimates of the exponent of the power function were an inverse function of interval size.