Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.

The characteristics of six species of living hollow-bearing trees and their importance for arboreal marsupials in the dry sclerophyll forests of southeast Queensland, Australia

Six species of trees located in the dry sclerophyll forests of southeast Queensland were studied to ascertain which was most suitable to be retained as hollow-bearing trees for nesting and denning by arboreal marsupials. Generally for all tree species, the number of entrances to hollows was positively correlated with the diameter at breast height (DBH) and the growth stage, and entrance diameters also increased in trees with a larger DBH. However, there were differences between the species; Corymbia citriodora had few hollows until the individuals were very large while Eucalyptus crebra had low numbers of hollows throughout its entire size range. It was concluded that a mixture of tree species provided a range of hollow sizes and positions that would be suitable for nesting and denning by arboreal marsupials in those forests. There were large differences between tree species in the relationship between tree size and estimated age. Five of the tree species took between 186 and 230 years to begin to produce hollows while E. crebra took up to 324 years. This suggests that tree species other than E. crebra may be the most preferred for retention in areas where hollow-bearing tree densities are lower than the prescribed level. Other data also suggests there are likely to be enough trees in larger size classes that would begin to form hollows within the next 50 years to compensate for an expected loss of hollow-bearing stags during that same period. In terms of forest operation, the retention of six hollow-bearing trees/ha would represent an estimated loss of 7.3-15% wood production. (C) 2003 Elsevier Science B.V. All rights reserved.

Emergence of joint attention: Relationships between gaze following, social referencing, imitation, and naming in infancy

The authors investigated the extent to which the joint-attention behaviors of gaze following, social referencing, and object-directed imitation were related to each other and to infants vocabulary development in a sample of 60 infants between the ages of 8 and 14 months. Joint-attention skills and vocabulary development were assessed in a laboratory setting. Split-half reliability analyses on the joint-attention measures indicated that the tasks reliably assessed infants' capabilities. In the main analysis, no significant correlations were found among the joint-attention behaviors except for a significant relationship between gaze following and the number of names in infants' productive vocabularies. The overall pattern of results did not replicate results of previous studies (e.g., M. Carpenter, K. Nagell, & M. Tomasello, 1998) that found relationships between various emerging joint-attention behaviors.