The Natural Statistics of Audiovisual Speech

Humans, like other animals, are exposed to a continuous stream of signals, which are dynamic, multimodal, extended, and time varying in nature. This complex input space must be transduced and sampled by our sensory systems and transmitted to the brain where it can guide the selection of appropriate actions. To simplify this process, it's been suggested that the brain exploits statistical regularities in the stimulus space. Tests of this idea have largely been confined to unimodal signals and natural scenes. One important class of multisensory signals for which a quantitative input space characterization is unavailable is human speech. We do not understand what signals our brain has to actively piece together from an audiovisual speech stream to arrive at a percept versus what is already embedded in the signal structure of the stream itself. In essence, we do not have a clear understanding of the natural statistics of audiovisual speech. In the present study, we identified the following major statistical features of audiovisual speech. First, we observed robust correlations and close temporal correspondence between the area of the mouth opening and the acoustic envelope. Second, we found the strongest correlation between the area of the mouth opening and vocal tract resonances. Third, we observed that both area of the mouth opening and the voice envelope are temporally modulated in the 2–7 Hz frequency range. Finally, we show that the timing of mouth movements relative to the onset of the voice is consistently between 100 and 300 ms. We interpret these data in the context of recent neural theories of speech which suggest that speech communication is a reciprocally coupled, multisensory event, whereby the outputs of the signaler are matched to the neural processes of the receiver

he Direction of Spontaneous Magnetisation of Lanthanide Ions at a Site of Cubic Symmetry

The zero temperature direction of spontaneous magnetisation of lanthanide ions at a site of cubic symmetry is investigated as a function of the electrostatic and magnetic interactions. For all the values of J between J = 3 and J = 8, two-dimensional diagrams giving the orientation of spontaneous magnetisation are obtained as a function of the parameters R representing the relative strength of the magnetic to electrostatic interaction and the parameter x representing the relative strength of the fourth to the sixth order terms in the crystal field. The boundaries between regions of the parameter space with different directions of spontaneous magnetisation are investigated. It is found that at some boundaries there is a gradual rotation of the direction of spontaneous magnetisation and that at other boundaries there is a sudden change of orientation of spontaneous magnetisation at a critical value of the (R,x) parameters. Two types of behaviour are observed when there is a critical value of (R,x). There are boundaries where there is at the critical value a degenerate plane in which all the orientations can be direction of spontaneous magnetisation and some boundaries where two different principal crystallographic axes can be direction of spontaneous magnetisation at the critical value. In the latter case there is a region near the boundary where an unstable equilibrium orientation for the magnetisation can be found