Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

Bathorhodopsin structure in the room-temperature rhodopsin photosequence: picosecond time-resolved coherent anti-Stokes Raman scattering.

Structural changes in the retinal chromophore during the formation of the bathorhodopsin intermediate (bathoRT) in the room-temperature rhodopsin (RhRT) photosequence (i.e., vision) are examined using picosecond time-resolved coherent anti-Stokes Raman scattering. Specifically, the retinal structure assignable to bathoRT following 8-ps excitation of RhRT is measured via vibrational Raman spectroscopy at a 200-ps time delay where the only intermediate present is bathoRT. Significant differences are observed between the C=C stretching frequencies of the retinal chromophore at low temperature where bathorhodopsin is stabilized and at room temperature where bathorhodopsin is a transient species in the RhRT photosequence. These vibrational data are discussed in terms of the formation of bathoRT, an important step in the energy storage/transduction mechanism of RhRT.

AtGRP7, a nuclear RNA-binding protein as a component of a circadian-regulated negative feedback loop in Arabidopsis thaliana

The endogenous clock that drives circadian rhythms is thought to communicate temporal information within the cell via cycling downstream transcripts. A transcript encoding a glycine-rich RNA-binding protein, Atgrp7, in Arabidopsis thaliana undergoes circadian oscillations with peak levels in the evening. The AtGRP7 protein also cycles with a time delay so that Atgrp7 transcript levels decline when the AtGRP7 protein accumulates to high levels. After AtGRP7 protein concentration has fallen to trough levels, Atgrp7 transcript starts to reaccumulate. Overexpression of AtGRP7 in transgenic Arabidopsis plants severely depresses cycling of the endogenous Atgrp7 transcript. These data establish both transcript and protein as components of a negative feedback circuit capable of generating a stable oscillation. AtGRP7 overexpression also depresses the oscillation of the circadian-regulated transcript encoding the related RNA-binding protein AtGRP8 but does not affect the oscillation of transcripts such as cab or catalase mRNAs. We propose that the AtGRP7 autoregulatory loop represents a “slave” oscillator in Arabidopsis that receives temporal information from a central “master” oscillator, conserves the rhythmicity by negative feedback, and transduces it to the output pathway by regulating a subset of clock-controlled transcripts.

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems.