Linear mapping of numbers onto space requires attention,Cognition, 3 (122), 454-459.

Mapping of number onto space is fundamental to mathematics and measurement. Previous research suggests that while typical adults with mathematical schooling map numbers veridically onto a linear scale, pre-school children and adults without formal mathematics training, as well as individuals with dyscalculia, show strong compressive, logarithmic-like non-linearities when mapping both symbolic and non-symbolic numbers onto the numberline. Here we show that the use of the linear scale is dependent on attentional resources. We asked typical adults to position clouds of dots on a numberline of various lengths. In agreement with previous research, they did so veridically under normal conditions, but when asked to perform a concurrent attentionally-demanding conjunction task, the mapping followed a compressive, non-linear function. We model the non-linearity both by the commonly assumed logarithmic transform, and also with a Bayesian model of central tendency. These results suggest that veridical representation numerosity requires attentional mechanisms.

Optimal Encoding of Interval Timing in Expert Percussionists, J Neurosci, 3 (32), 1056-1060.

We measured temporal reproduction in human subjects with various levels of musical expertise: expert drummers, string musicians, and non-musicians. While duration reproduction of the non-percussionists showed a characteristic central tendency or regression to the mean, drummers responded veridically. Furthermore, when the stimuli were auditory tones rather than flashes, all subjects responded veridically. The behavior of all three groups in both modalities is well explained by a Bayesian model that seeks to minimize reproduction errors by incorporating a central tendency prior, a probability density function centered at the mean duration of the sample. We measured separately temporal precision thresholds with a bisection task; thresholds were twice as low in drummers as in the other two groups. These estimates of temporal precision, together with an adaptable Bayesian prior, predict well the reproduction results and the central tendency strategy under all conditions and for all subject groups. These results highlight the efficiency and flexibility of sensorimotor mechanisms estimating temporal duration.

“Non-retinotopic processing” in Ternus motion displays modeled by spatiotemporal filters,J Vis, 1 (12),

Recently, M. Boi, H. Ogmen, J. Krummenacher, T. U. Otto, & M. H. Herzog (2009) reported a fascinating visual effect, where the direction of apparent motion was disambiguated by cues along the path of apparent motion, the Ternus-Pikler group motion, even though no actual movement occurs in this stimulus. They referred to their study as a “litmus test” to distinguish “non-retinotopic” (motion-based) from “retinotopic” (retina-based) image processing. We adapted the test to one with simple grating stimuli that could be more readily modeled and replicated their psychophysical results quantitatively with this stimulus. We then modeled our experiments in 3D (x, y, t) Fourier space and demonstrated that the observed perceptual effects are readily accounted for by integration of information within a detector that is oriented in space and time, in a similar way to previous explanations of other motion illusions. This demonstration brings the study of Boi et al. into the more general context of perception of moving objects.

Perception of duration in the parvocellular system, Front Integr Neurosci 6:14

Both theoretical and experimental evidence suggests that duration perception is mediated preferentially by the color-blind but high temporally sensitive luminance pathway. In this experiment we tested whether color modulated stimuli and high spatial frequency luminance modulated stimuli, which are known to be relayed mostly by the slow parvocellular system, are able to elicit reliable sense of duration. We show that ramped color modulated stimuli seem to last less than luminance modulated stimuli matched for visibility. The effect is large, about 200 ms and is constant at all durations tested (range 500–1100 ms). However, high spatial frequency luminance stimuli obtain duration matches similar to those of low spatial frequency luminance modulated stimuli. The results at various levels of contrast and temporal smoothing indicate that equiluminant stimuli have higher contrast thresholds to activate the mechanisms which time visual stimuli. Overall the results imply that both the magnocellular and the parvocellular systems access reliably the timing mechanisms with a difference only in the way these are engaged

The effects of cross-sensory attentional demand on subitizing and on mapping number onto space,Vision Res,

Various aspects of numerosity judgments, especially subitizing and the mapping of number onto space, depend strongly on attentional resources. Here we use a dual-task paradigm to investigate the effects of cross-sensory attentional demands on visual subitizing and spatial mapping. The results show that subitizing is strongly dependent on attentional resources, far more so than is estimation of higher numerosities. But unlike many other sensory tasks, visual subitizing is equally affected by concurrent attentionally demanding auditory and tactile tasks as it is by visual tasks, suggesting that subitizing may be amodal. Mapping number onto space was also strongly affected by attention, but only when the dual-task was in the visual modality. The non-linearities in numberline mapping under attentional load are well explained by a Bayesian model of central tendency.

Blindsight in children with congenital and acquired cerebral lesions, Cortex (published online 10 August 2012)

It has been shown that unconscious visual function can survive lesions to optical radiations and/or primary visual cortex (V1), a phenomenon termed “blindsight”. Studies on animal models (cat and monkey) show that the age when the lesion occurs determines the extent of residual visual capacities. Much less is known about the functional and underlying neuronal repercussions of early cortical damage in humans. We measured sensitivity to several visual tasks in four children with congenital unilateral brain lesions that severely affected optic radiations, and in another group of three children with similar lesions, acquired in childhood. In two of the congenital patients, we measured blood oxygenation level dependent (BOLD) activity in response to stimulation of each visual field quadrants. Results show clear evidence of residual unconscious processing of position, orientation and motion of visual stimuli displayed in the scotoma of congenitally lesioned children, but not in the children with acquired lesions. The calcarine cortical BOLD responses were abnormally elicited by stimulation of the ipsilateral visual field and in the scotoma region, demonstrating a profound neuronal reorganization. In conclusion, our data suggest that congenital lesions can trigger massive reorganization of the visual system to alleviate functional effects of early brain insults.