A traditional line of work starting with the Gestalt school has shown that patterns vary in strength and salience; a difference in “Perceptual goodness.” The Holographic weight of evidence model quantifies goodness of visual regularities. The key formula states that W = E/N, where E is number of holographic identities in a pattern and N is number of elements. We tested whether W predicts the amplitude of the neural response to regularity in an extrastriate symmetry-sensitive network. We recorded an Event Related Potential (ERP) generated by symmetry called the Sustained Posterior Negativity (SPN). First, we reanalyzed the published work and found that W explained most variance in SPN amplitude. Then in four new studies, we confirmed specific predictions of the holographic model regarding 1) the differential effects of numerosity on reflection and repetition, 2) the similarity between reflection and Glass patterns, 3) multiple symmetries, and 4) symmetry and anti-symmetry. In all cases, the holographic approach predicted SPN amplitude remarkably well; particularly in an early window around 300–400 ms post stimulus onset. Although the holographic model was not conceived as a model of neural processing, it captures many details of the brain response to symmetry.

No abstract

Animals can perceive the numerosity of sets of visual elements. Qualitative and quantitative similarities in different species suggest the existence of a shared system (approximate number system). Biases associated with sensory properties are informative about the underlying mechanisms. In humans, regular spacing increases perceived numerosity (regular-random numerosity illusion). This has led to a model that predicts numerosity based on occupancy (a measure that decreases when elements are close together). We used a procedure in which observers selected one of two stimuli and were given feedback with respect to whether the choice was correct. One configuration had 20 elements and the other 40, randomly placed inside a circular region. Participants had to discover the rule based on feedback. Because density and clustering covaried with numerosity, different dimensions could be used. After reaching a criterion, test trials presented two types of configurations with 30 elements. One type had a larger interelement distance than the other (high or low clustering). If observers had adopted a numerosity strategy, they would choose low clustering (if reinforced with 40) and high clustering (if reinforced with 20). A clustering or density strategy predicts the opposite. Human adults used a numerosity strategy. Chicks were tested using a similar procedure. There were two behavioral measures: first approach response and final circumnavigation (walking behind the screen). The prediction based on numerosity was confirmed by the first approach data. For chicks, one clear pattern from both responses was a preference for the configurations with higher clustering. (PsycINFO Database Record

In four experiments we investigated the Solitaire illusion. In this illusion, most observers see as more numerous a set of dots that forms a single central group, compared to dots on the outside of that group. We confirmed and extended the effect to configurations with much higher numerosity than the original and of various colours. Contrary to prediction, separating the two groups, so that they are presented side by side, reduced but did not abolish or reverse the illusion. In this illusion, therefore, neither total size of the region (area), not average distance of the elements has the expected effect. In Experiments 3 and 4 we eliminated the regularity of the pattern, by sampling 50% (Exp 3) or only a 10% (Exp 4) of the elements. These produces quasi-random configurations. For these configurations the bias for the inner groups was still present, and it was only eliminated when the groups were shown as separate. However, the effect never reversed (no bias for the outer group, despite its larger area). We conclude that the Solitaire illusion is evidence of a strong bias in favour of centrally located elements, a bias that can overcome other factors.

Observers can quickly estimate the quantity of sets of visual elements. Many aspects of this ability have been studied and the underlying system has been called the Approximate Number Sense (Dehaene, 2011). Specific visual properties, such as size and clustering of the elements, can bias an estimate. For intermediate numerical quantities at low density (above five, but before texturization), human performance is predicted by a model based on the region of influence of elements (occupancy model: Allïk & Tuulmets, 1991). For random 2D configurations we computed ten indices based on graph theory, and we compared them with the occupancy model: independence number, domination, connected components, local clustering coefficient, global clustering coefficient, random walk, eigenvector centrality, maximum clique, total degree of connectivity, and total edge length. We made comparisons across a range of parameters, and we varied the size of the region of influence around each element. The analysis of the pattern of correlations suggests two main groups of graph-based measures. The first group is sensitive to the presence of local clustering of elements, the second seems more sensitive to density and the way information spreads in graphs. Empirical work on perception of numerosity may benefit from comparing, or controlling for, these properties.

No abstract

No abstract

Los Angeles: Sage 256 pages, ISBN 9781452268392, £20.99 (spiral bound) This book sets out to provide the reader with an easy overview of how to use the American Psychological Association's (APA) writing guidelines and referencing style. The APA style is commonly used by psychologists and other social and behaviour-related disciplines. For psychologists in particular, it is the 'definitive' guide on how to structure your research paper in a publishable format.The book consists of six sections, of which the first two are relatively generic in nature. The first section is an overview of what APA style is as well as a visual table of contents (a QuickFinder). The QuickFinder is a simple (and creative) way of ensuring that readers can easily find what they need to within the book. It consists of a sample paper that is annotated with APA style examples and the page numbers where you can find further information about the particular example. The underlying idea is that the reader may not know the correct terminology for what they wish to do and hence will be unable to look it up in a traditional index. Equally it is also possible that the reader is unaware of a particular rule and will therefore not know to look for it at all. Both the previous examples are problems that the QuickFinder overcomes beautifully.In section two the authors tackle general tips about writing such as when to use active or passive voice, common grammar mistakes, paraphrasing, and biased language issues. This section is clear and concise even though it is far too brief to be truly helpful for those who need a lot of support with issues particularly related to grammar and writing style. The authors recognise this and do suggest other books that may be useful to consult if needed.In the third section of this book the reader is finally faced with more specific details about the APA style. It is somewhat unfortunate that the first chapter in this section (7) is titled Whodunit (or Said It)? as it distracts somewhat from how nice the rest of the book is. Presumably such a title is to keep student readers amused. Having said that the section is otherwise great, it is well structured, and guides the reader easily through topics such as how to use citations, how to format your method section, and how to write your references properly. There is also a chapter in this section on statistics that could possibly have been a little longer and more in-depth. Presenting statistics in a clear and concise manner is something that students often struggle with. Consequently it would have been nice if the authors had provided a few more examples of commonly occurring problems. Nevertheless, the statistically based chapter has some great parts that students should really benefit from reading such as the section on effect size and power. It is really clearly explained and should not leave anybody in doubt about how and why it should be reported.Section four provides an overview of how to present your work in APA format. This section takes a look at when to use nume...