The principle of canonical orientation: a cross-linguistic study

abstractThis paper presents a cross-linguistic investigation of a constraint on the use on intrinsic frames of reference proposed by Levelt (1984, 1996). This proposed constraint claims that use of intrinsic frames when the ground object is in non-canonical position is blocked due to conflict with gravitational-based reference frames. Regression models of the data from Arabic, K’iche’, Spanish, Yucatec, and Zapotec suggest that this constraint is valid across languages. However, the strength at which the constraint operates is predicted by the frequency of canonical intrinsic frames in the particular language. The ratio of the incidence of intrinsic usage with canonical vs. non-canonical orientation appears to be remarkably uniform across languages, which suggests the possibility of a strong cognitive universal.

Skew Spectra of Oriented Bipartite Graphs

A graph $G$ is said to have a parity-linked orientation $\phi$ if every even cycle $C_{2k}$ in $G^{\phi}$ is evenly (resp. oddly) oriented whenever $k$ is even (resp. odd). In this paper, this concept is used to provide an affirmative answer to the following conjecture of D. Cui and Y. Hou [D. Cui, Y. Hou, On the skew spectra of Cartesian products of graphs, Electronic J. Combin. 20(2):#P19, 2013]: Let $G=G(X,Y)$ be a bipartite graph. Call the $X\rightarrow Y$ orientation of $G,$ the canonical orientation. Let $\phi$ be any orientation of $G$ and let $Sp_S(G^{\phi})$ and $Sp(G)$ denote respectively the skew spectrum of $G^{\phi}$ and the spectrum of $G.$ Then $Sp_S(G^{\phi}) = {\bf{i}} Sp(G)$ if and only if $\phi$ is switching-equivalent to the canonical orientation of $G.$ Using this result, we determine the switch for a special family of oriented hypercubes $Q_d^{\phi},$ $d\geq 1.$ Moreover, we give an orientation of the Cartesian product of a bipartite graph and a graph, and then determine the skew spectrum of the resulting oriented product graph, which generalizes a result of Cui and Hou. Further this can be used to construct new families of oriented graphs with maximum skew energy.

Ecological Aspects of Mental Rotation Around the Vertical and Horizontal Axis

Rotation of both natural and man-made objects most commonly requires rotation around the vertical rather than the horizontal axis because it is relatively rare that we need to rotate, e.g., trees, mountains, chairs or vehicles around their horizontal axis in order to match images to their canonical orientation. Waszak, Drewing, and Mausfeld (2005) demonstrated the importance of a gravitationally defined vertical axis and the visual context within which objects occur, when performing mental rotations. We extended their findings in a between-subject design by asking 406 subjects to rotate wireframe cube figures around either the vertical axis or around the horizontal axis. Both male and female subjects performed significantly better when rotating objects around the vertical axis. Males performed better than females in both conditions, and there was no interaction between axis of rotation and sex.

Minimal 4-manifolds for groups of cohomological dimension 2

We show that if π is a group with a finite 2-dimensional Eilenberg-Mac Lane complex then the minimum of the Euler characteristics of closed 4-manifolds with fundamental group π is 2χ(K(π, 1)). If moreover M is such a manifold realizing this minimum then π2(M) ≅ Similarly, if π is a PD3-group and w1(M) is the canonical orientation character of π then χ(M)≧l and π2(M) is stably isomorphic to the augmentation ideal of Z[π].