We study generalizations of the forest fire model introduced in [4] and [10] by allowing the rates at which the trees grow to depend on their location, introducing long-range burning, as well as a continuous-space generalization of the model. We establish that in all the models in consideration the expected time required to reach a site at distance x from the origin is of order $(\!\log x)^{(\!\log 2)^{-1}+\delta}$ for any $\delta>0$ .

We quantified and compared the effect of element spacing on contour integration between the achromatic (Ach), red–green (RG), and blue–yellow (BY) mechanisms. The task requires the linking of orientation across space to detect a contour in a stimulus composed of randomly oriented Gabor elements (1.5 cpd, σ = 0.17 deg), measured using a temporal 2AFC method. A contour of ten elements was pasted into a 10 × 10 cells array, and background elements were randomly positioned within the available cells. The effect of element spacing was investigated by varying the mean interelement distance between two and six times the period of the Gabor elements (λ = 0.66 deg) while the total number of elements was fixed. Contour detection was measured as a function of its curvature for jagged contours and for closed contours. At all curvatures, we found that performance for chromatic mechanisms declines more steeply with the increase in element separation than does performance for the achromatic mechanism. Averaged critical element separations were 4.6 ± 0.7, 3.6 ± 0.4, and 2.9 ± 0.2 deg for Ach, BY, and RG mechanisms, respectively. These results suggest that contour integration by the chromatic mechanisms relies more on short-range interactions in comparison to the achromatic mechanism. In a further experiment, we looked at the combined effect of element size and element separation in contour integration for the Ach mechanism.

Visual stimulation of zones extending beyond the classical receptive field can modulate the contrast gain of neurons in the lateral geniculate nucleus (LGN) of cats, but little is known about the effect of extra-classical visual stimulation on the LGN of primates. Hence, we compare the effect of long-range interactions in parvocellular and magnocellular LGN layers of the marmoset monkey Callithrix jacchus using optimal, incremental spots flashed on the classical receptive field either alone or simultaneously with the shift of a grating (98% contrast; 0.1 cycles/deg) confined to a peripheral annulus (radii: 5–15 deg). The contrast required to drive the response halfway to saturation (c50) of most LGN neurons was raised by remote pattern shifts. The c50 ratio [(shift+spot)/spot] in OFF-center magnocellular neurons was significantly higher than in OFF-center parvocellular neurons. OFF-center magnocellular neurons closer to the fovea (<10 deg eccentricity) tended to have a higher c50 ratio than in more peripheral neurons. A significant drop in visual sensitivity to 25% contrast spots was observed during remote motion: d′ fell from 1.8 to 1.4 in parvocellular neurons and from 2.2 to 1.7 in magnocellular neurons. Such long-range interactions produce a reduction in visual sensitivity by changing the gain of the geniculate relay and point to an inhibitory, motion-sensitive extra-classical receptive field in both parvocellular and magnocellular pathways, which may be involved in saccadic suppression and attentional mechanisms in early vision.

In previous work, we have shown that sudden image displacements well outside the classical receptive field modulate the visual sensitivity of LGN relay cells. Here we report the effect of image displacements on the response versus contrast function. The stimuli consisted of a central spot of optimal size and polarity (contrast range: 3–98%), flashed alone or in the presence of a peripheral annulus (radii: 5–15 deg) containing a low spatial-frequency grating displaced at saccade-like velocities (shift). The most consistent effect of the shift on the response to a central spot was to reduce the responsiveness of Y relay cells and, to a lesser extent, of X relay cells. The reduction in responsiveness was primarily a divisive rather than a subtractive effect and could be modelled by assuming that a greater contrast was required to produce a given excitatory response. In the absence of a central spot, remote motion had inhibitory effects on the firing rates of the majority of relay cells, but its effect on retinal ganglion cells was mainly excitatory. When the shifting grating covered the classical receptive field and its periphery, facilitatory effects or suppressive effects, depending on the spatial phase of the pattern, were observed in both retinal and geniculate cells. Remote motion strongly suppresses the responsiveness of relay cells to stimuli within the classical receptive field. This suppressive effect involves intrageniculate processing and is primarily associated with a reduction in contrast gain. It is likely that shift suppression contributes to the loss of visual sensitivity observed in saccadic suppression.