A spatial frequency spectral peakedness model predicts discrimination performance of regularity in dot patterns.

Subjective assessments of spatial regularity are common in everyday life and also in science, for example in developmental biology. It has recently been shown that regularity is an adaptable visual dimension. It was proposed that regularity is coded via the peakedness of the distribution of neural responses across receptive field size. Here, we test this proposal for jittered square lattices of dots. We examine whether discriminability correlates with a simple peakedness measure across different presentation conditions (dot number, size, and average spacing). Using a filter-rectify-filter model, we determined responses across scale. Consistently, two peaks are present: a lower frequency peak corresponding to the dot spacing of the regular pattern and a higher frequency peak corresponding to the pattern element (dot). We define the "peakedness" of a particular presentation condition as the relative heights of these two peaks for a perfectly regular pattern constructed using the corresponding dot size, number and spacing. We conducted two psychophysical experiments in which observers judged relative regularity in a 2-alternative forced-choice task. In the first experiment we used a single reference pattern of intermediate regularity and, in the second, Thurstonian scaling of patterns covering the entire range of regularity. In both experiments discriminability was highly correlated with peakedness for a wide range of presentation conditions. This supports the hypothesis that regularity is coded via peakedness of the distribution of responses across scale.

Difference magnitude is not measured by discrimination steps for order of point patterns.

We have shown in previous work that the perception of order in point patterns is consistent with an interval scale structure (Protonotarios, Baum, Johnston, Hunter, & Griffin, 2014). The psychophysical scaling method used relies on the confusion between stimuli with similar levels of order, and the resulting discrimination scale is expressed in just-noticeable differences (jnds). As with other perceptual dimensions, an interesting question is whether suprathreshold (perceptual) differences are consistent with distances between stimuli on the discrimination scale. To test that, we collected discrimination data, and data based on comparison of perceptual differences. The stimuli were jittered square lattices of dots, covering the range from total disorder (Poisson) to perfect order (square lattice), roughly equally spaced on the discrimination scale. Observers picked the most ordered pattern from a pair, and the pair of patterns with the greatest difference in order from two pairs. Although the judgments of perceptual difference were found to be consistent with an interval scale, like the discrimination judgments, no common interval scale that could predict both sets of data was possible. In particular, the midpattern of the perceptual scale is 11 jnds away from the ordered end, and 5 jnds from the disordered end of the discrimination scale.

Flat clathrin lattices: stable features of the plasma membrane.

Clathrin-mediated endocytosis (CME) is a fundamental property of eukaryotic cells. Classical CME proceeds via the formation of clathrin-coated pits (CCPs) at the plasma membrane, which invaginate to form clathrin-coated vesicles, a process that is well understood. However, clathrin also assembles into flat clathrin lattices (FCLs); these structures remain poorly described, and their contribution to cell biology is unclear. We used quantitative imaging to provide the first comprehensive description of FCLs and explore their influence on plasma membrane organization. Ultrastructural analysis by electron and superresolution microscopy revealed two discrete populations of clathrin structures. CCPs were typified by their sphericity, small size, and homogeneity. FCLs were planar, large, and heterogeneous and present on both the dorsal and ventral surfaces of cells. Live microscopy demonstrated that CCPs are short lived and culminate in a peak of dynamin recruitment, consistent with classical CME. In contrast, FCLs were long lived, with sustained association with dynamin. We investigated the biological relevance of FCLs using the chemokine receptor CCR5 as a model system. Agonist activation leads to sustained recruitment of CCR5 to FCLs. Quantitative molecular imaging indicated that FCLs partitioned receptors at the cell surface. Our observations suggest that FCLs provide stable platforms for the recruitment of endocytic cargo.

An absolute interval scale of order for point patterns.

Human observers readily make judgements about the degree of order in planar arrangements of points (point patterns). Here, based on pairwise ranking of 20 point patterns by degree of order, we have been able to show that judgements of order are highly consistent across individuals and the dimension of order has an interval scale structure spanning roughly 10 just-notable-differences (jnd) between disorder and order. We describe a geometric algorithm that estimates order to an accuracy of half a jnd by quantifying the variability of the size and shape of spaces between points. The algorithm is 70% more accurate than the best available measures. By anchoring the output of the algorithm so that Poisson point processes score on average 0, perfect lattices score 10 and unit steps correspond closely to jnds, we construct an absolute interval scale of order. We demonstrate its utility in biology by using this scale to quantify order during the development of the pattern of bristles on the dorsal thorax of the fruit fly.