An n-dimensional Weber Law and the Corresponding Fechner Law

Radial distance determination in the rat vibrissal system and the effects of Weber's law

Rats rhythmically tap and brush their vibrissae (whiskers) against objects to tactually explore the environment. To extract a complex feature such as the contour of an object, the rat must at least implicitly estimate radial object distance, that is, the distance from the base of the vibrissa to the point of object contact. Radial object distance cannot be directly measured, however, because there are no mechanoreceptors along the vibrissa. Instead, the mechanical signals generated by the vibrissa's interaction with the environment must be transmitted to mechanoreceptors near the vibrissa base. The first part of this paper surveys the different mechanical methods by which the rat could determine radial object distance. Two novel methods are highlighted: one based on measurement of bending moment and axial force at the vibrissa base, and a second based on measurement of how far the vibrissa rotates beyond initial contact. The second part of the paper discusses the application of Weber's law to two methods for radial distance determination. In both cases, Weber's law predicts that the rat will have greatest sensing resolution close to the vibrissa tip. These predictions could be tested with behavioural experiments that measure the perceptual acuity of the rat.

The detection of multisensory stimuli in an orthogonal sensory space

The detection of a stimulus can be considerably facilitated if the stimulus engages two or more sensory modalities simultaneously. This phenomenon, commonly referred to as multisensory (or cross-modal) facilitation, has been demonstrated behaviorally in cats and humans. A number of rules are thought to govern this phenomenon. These rules state that strong facilitation is to be expected only if the two sensory modalities are stimulated simultaneously and at the same place, and if the stimuli themselves are weak. However, these rules are not sufficient to allow accurate predictions of multimodal stimulus detection probabilities directly from physical stimulus parameters. Here we show that such predictions are possible on the basis of a simple and biologically plausible psychophysical model, which relates the detection of audio-visual, audio-tactile or visual-tactile stimuli to the Euclidean distance that these stimuli span in an orthogonal sensory space.