Those groups r which act properly discontinuously and aillnely on II?’ with compact fundamental domain are classified. First it is shown that such a group f contains a solvable subgroup of finite index, thus establishing a conjecture of Auslander in dimension three. Then unimodular simply transitive alTine actions on IR’ are classified; this leads to a classification of atTine crystallographic ...

Let M be an ℵ 0 -categorical structure and assume that has no algebraicity weak elimination of imaginaries. Generalizing classical theorems de Finetti Ryll-Nardzewski, we show any ergodic, Aut(M)-invariant measure on [0,1] is a product measure. We also investigate the action Aut(M) compact space LO(M) linear orders M. If moreover Aut(M)↷M transitive, prove Aut(M)↷LO(M) either fixed point or uni...

We associate a 2-complex to the following data: a presentation of a semigroup S and a transitive action of S on a set V by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient condition is given for the 2-complex to be simply connected. As a consequence we obtain simple topological proofs of results on presentations of Schüt...

An equivalent relation between transitive 1-factorizations of arctransitive graphs and factorizations of their automorphism groups is established. This relation provides a method for constructing and characterizing transitive 1-factorizations for certain classes of arc-transitive graphs. Then a characterization is given of 2-arc-transitive graphs which have transitive 1factorizations. In this c...

The recognition of actions that involve the use of objects has remained a challenging task. In this paper, we present a hierarchical selforganizing neural architecture for learning to recognize transitive actions from RGB-D videos. We process separately body poses extracted from depth map sequences and object features from RGB images. These cues are subsequently integrated to learn action–objec...

In Floyd-Hoare logic, programs are dynamic while assertions are static (hold at states). In action logic the two notions become one, with programs viewed as on-the-fly assertions whose truth is evaluated along intervals instead of at states. Action logic is an equational theory ACT conservatively extending the equational theory REG of regular expressions with operations preimplication a+b (had ...

In this paper, we determine all of connected normal edge-transitive Cayley graphs on non-abelian groups with order $4p^2$, where $p$ is a prime number.

Can linguistic structures influence how people perceive and remember causal events? Using a change-detection method, we presented participants with direct causal scenes paired with either transitive (He stretched the toy) or periphrastic sentences (He made the toy stretch.) Participants then viewed movies with changes to the manner of action (stretching the toy with palms up vs. down), the resu...

In this paper we give a classification of a family of symmetric graphs with complete 2-arc transitive quotients. Of particular interest are two subfamilies of graphs which admit an arc-transitive action of a projective linear group. The graphs in these subfamilies can be defined in terms of the cross ratio of certain 4-tuples of elements of a finite projective line, and thus may be called the s...

When toddlers view an event while hearing a novel verb, the verb's syntactic context has been shown to help them identify its meaning. The current work takes this finding one step further to reveal that even in the absence of an accompanying event, syntactic information supports toddlers' identification of verb meaning. Two-year-olds were first introduced to dialogues incorporating novel verbs ...