Goldberg, Fuller, Caspar, Klug and Coxeter and a general approach to local symmetry-preserving operations

Cubic polyhedra with icosahedral symmetry where all faces are pentagons or hexagons have been studied in chemistry and biology as well as mathematics. In chemistry one of these is buckminsterfullerene, a pure carbon cage with maximal symmetry, whereas in biology they describe the structure of spherical viruses. Parameterized operations to construct all such polyhedra were first described by Goldberg in 1937 in a mathematical context and later by Caspar and Klug -- not knowing about Goldberg's work -- in 1962 in a biological context. In the meantime Buckminster Fuller also used subdivided icosahedral structures for the construction of his geodesic domes. In 1971 Coxeter published a survey article that refers to these constructions. Subsequently, the literature often refers to the Goldberg-Coxeter construction. This construction is actually that of Caspar and Klug. Moreover, there are essential differences between this (Caspar/Klug/Coxeter) approach and the approaches of Fuller and of Goldberg. We will sketch the different approaches and generalize Goldberg's approach to a systematic one encompassing all local symmetry-preserving operations on polyhedra

Generation of local symmetry-preserving operations on polyhedra

We introduce a new practical and more general definition of local symmetry-preserving operations on polyhedra. These can be applied to arbitrary embedded graphs and result in embedded graphs with the same or higher symmetry. With some additional properties we can restrict the connectivity, e.g. when we only want to consider polyhedra. Using some base structures and a list of 10 extensions, we can generate all possible local symmetry-preserving operations isomorph-free

Local orientation-preserving symmetry preserving operations on polyhedra

Unifying approaches by amongst others Archimedes, Kepler, Goldberg, Caspar and Klug, Coxeter, and Conway, and extending on a previous formalisation of the concept of local symmetry preserving (lsp) operations, we introduce a formal definition of local operations on plane graphs that preserve orientation-preserving symmetries, but not necessarily orientation-reversing symmetries. This operations include, e.g., the chiral Goldberg and Conway operations as well as all lsp operations. We prove the soundness of our definition as well as introduce an invariant which can be used to systematically construct all such operations. We also show sufficient conditions for an operation to preserve the connectedness of the plane graph to which it is applied

Enumeration of generalized fusenes

Generalized fusenes are structures that are similar to the hexagon based benzenoids and fusenes, except that also non-hexagonal faces are allowed. In this paper, a fast algorithm to enumerate generalized fusenes with given faces is given. The algorithm is fast enough to generate millions of non-isomorphic structures per second and is based on a two-step approach using the canonical construction path method and the homomorphism principle

Image memorability across longer time intervals

You may find some images easier to remember than others. Recent studies of visual memory have found remarkable levels of consistency for this inter-item variability across observers, suggesting that memorability can be considered an intrinsic image property. The current study replicated and extended previous results, while adopting a more traditional visual longterm memory task with retention intervals of 20 min, one day, and one week, as opposed to the previously used repeat-detection task, which typically relied on short retention intervals (5 min). Our memorability rank scores show levels of consistency across observers in line with those reported in previous research. They correlate strongly with previous quantifications and appear stable over time. Furthermore, we show that the way consistency of memorability scores increases with the number of responses per image follows the Spearman–Brown formula. Interestingly, our results also seem to show an increase in consistency with an increase in retention interval. Supported by simulated data, this effect is attributed to a decrease of extraneous influences on recognition over time. Finally, we also provide evidence for a log-linear, rather than linear, decline of the raw memorability scores over time, with more memorable images declining less strongly.status: publishe

Poster presentation: Are memorable images easier to categorize rapidly?

Some images we see stick in mind, while others fade. Recent studies of visual memory have found remarkable levels of consistency for this inter-item variability across observers (e.g., Isola 2011), suggesting that memorability can be considered an intrinsic image property. However, the visual features underlying memorability are not yet well understood. Investigating the relation between image memorability and inter-item variability in other visual tasks can provide more insight. Here, we asked whether an image that is easier to process and categorize is also more memorable. We used a rapid-scene categorization task and assessed whether there are consistent differences in difficulty between images in this task (defined as â categorizabilityâ ) and whether they correlate with memorability. We selected 14 scene categories and 44 images per category from a set previously quantified on memorability (Bylinskii 2015). Per trial, participants saw an image for a duration of 32 ms, followed by a mask of 80 ms. Next, a category label appeared on screen and the task was to indicate whether the label matched the image. For each participant, a random half of the scenes was presented as signal trials (i.e., label matches image), the other half as no-signal trials. For signal trials, we collected on average 79 responses per image. An imageâ s categorizability score was calculated as the proportion of correct responses on signal trials. The average categorizability score per category varied between .55 and .89. Thus, given the task context, some categories were considerably easier than others. For most categories, consistency scores were high (mean split-half Spearmanâ s rho up to .90), suggesting that categorizability is an intrinsic image property too. However, the predicted positive correlation between categorizability and memorability was not observed. This suggests that the ease with which an image can be categorized relies on features distinct from those involved in memorability.status: publishe

Get the Picture? Goodness of Image Organization Contributes to Image Memorability

According to Gestalt psychologists, goodness is a crucial variable for image organization. We hypothesized that these differences in goodness contribute to variability in image memorability. Building on this, we predicted that two characteristics of good organizations, (i) fast, efficient processing and (ii) robustness against transformations (e.g., shrinking), would be characteristic of memorable images. Two planned (Study 1, Study 2) and one follow-up (Study 3) study were conducted to test this. Study 1 operationalized fast processing as accuracy in a rapid-scene categorization task ("categorizability"). Study 2 operationalized robustness against shrinking as reaction time in a thumbnail search task ("shrinkability"). We used 44 real-life scene images of 14 semantic categories from a previous memorability study. Each image was assigned a categorizability and shrinkability score. The predicted positive relation between categorizability and memorability was not observed in Study 1. A post-hoc explanation attributed this null result to a masking role of image distinctiveness. Furthermore, memorable images were located faster in the thumbnail search task, as predicted, but Study 2 could not rule whether this was merely a result of their distinctiveness. To elucidate these results, Study 3 quantified the images on distinctiveness and statistically controlled for this variable in a reanalysis of Study 1 and Study 2. When distinctiveness was controlled for, categorizability and memorability did show a significant positive correlation. Moreover, the results also argued against the alternative explanation of the results of Study 2. Taken together, the results support the hypothesis that goodness of organization contributes to image memorability.status: Published onlin