To investigate how people anticipate and attempt to shape others’ self-regulatory efforts, this work examined the impact of abstract and concrete mindsets on attention to goal-relevant aspects of others’ situations. An abstract (relative to a concrete) mindset, by making accessible the cognitive operation of considering activities’ purpose (versus process) was predicted to focus attention on ho...

We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent various notions of computation self-assemble. Several open questions are also presented and motivated.

For every infinite sequence ω = x1x2 . . ., with xi ∈ {0, 1}, we construct an infinite 4-regular graph Xω. These graphs are precisely the Schreier graphs of the action of a certain self-similar group on the space {0, 1}∞. We solve the isomorphism and local isomorphism problems for these graphs, and determine their automorphism groups. Finally, we prove that all graphs Xω have intermediate growth.

We define the similarity boundary of a self-similar set and use it to analyze the properties of self-similar sets in the general setting of any complete metric space. The similarity boundary is an attempt at extending the concept of the topological boundary in a way that is consistent with our intuitive understanding of the term boundary. We also show how with the analysis of the similarity bou...

We introduce a class of formally self-dual additive codes over F4 as a natural analogue of binary formally self-dual codes, which is missing in the study of additive codes over F4. We define extremal formally self-dual additive codes over F4 and classify all such codes. Interestingly, we find exactly three formally self-dual additive (7, 27) odd codes over F4 with minimum distance d = 4, a bett...

Two studies examined the social basis of self-assessment for learning through the application of creative computer tools that can help students assess and self-correct their own learning. Students are not usually inclined to check their own answers, but they find it relatively motivating to catch other people’s mistakes. A total of 62 students, ranging in age from nine to 11, participated in tw...

Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," meaning that each portion can be considered a reduced-scale image of the whole. In that case, the degree of complication can be described by a quantity D that has many properties of a "dimension," though it is fractional; that is, it e...