Young children's performance on the balance scale: The influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains-transitivity and class inclusion-accounted for 93% of the age-related variance in balance scale scores. (C) 2002 Elsevier Science (USA).

The lateral line canal sensory organs of the Epaulette Shark (Hemiscyllium ocellatum)

Examination of the lateral line canals in the Epaulette Shark reveals a much more differentiated sensory system than previously reported from any elasmobranch. Two main types of lateral line canals are found. In one type rounded patches of sensory epithelia are separated by elevations of the canal floor. The other type is a straight canal without restrictions and with an almost continuous sensory epithelium. In addition, we found epithelia (type A) with very long apical microvilli on the supporting cells. These microvilli reach beyond the stereovilli of the hair cells. Another type (B) of sensory epithelium has short microvilli on the supporting cells. In this latter type of epithelium the stereovilli of the hair cells are comparatively tall and reach out beyond the supporting cell microvilli. New hair cells are found widely in both types of sensory epithelia. These always occur as single cells, unlike those described in teleost lateral line canal sensory epithelia where new hair cells seem to form in pairs. Dying hair cells are also widespread, indicating a continuous turnover of hair cells.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.