Crow's nest, Kangaroo Point House, Kangaroo Point, Brisbane

Deck and seating overlooking the river.

Crow's nest, Kangaroo Point House, Kangaroo Point, Brisbane

Deck and seating overlooking river.

Outdoor room, Kangaroo Point House, Kangaroo Point, Brisbane

Looking towards section of original house from outdoor room area. Hand-made spotted gum columns on edge of outdoor room on right.

Crow's nest, Kangaroo Point House, Kangaroo Point, Brisbane

Deck and seating overlooking river.

Battened roof to outdoor room, Kangaroo Point House, Kangaroo Point, Brisbane

Timber battened concave roof and supporting structure over outdoor room area.

Outdoor room, Kangaroo Point House, Kangaroo Point, Brisbane

Dining setting, sculptures, timber columns and curved roof in outdoor room

Crow's nest, Kangaroo Point House, Kangaroo Point, Brisbane

Structure to underside of deck and seating area.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Parameter setting and statistical learning

Three main models of parameter setting have been proposed: the Variational model proposed by Yang (2002; 2004), the Structured Acquisition model endorsed by Baker (2001; 2005), and the Very Early Parameter Setting (VEPS) model advanced by Wexler (1998). The VEPS model contends that parameters are set early. The Variational model supposes that children employ statistical learning mechanisms to decide among competing parameter values, so this model anticipates delays in parameter setting when critical input is sparse, and gradual setting of parameters. On the Structured Acquisition model, delays occur because parameters form a hierarchy, with higher-level parameters set before lower-level parameters. Assuming that children freely choose the initial value, children sometimes will miss-set parameters. However when that happens, the input is expected to trigger a precipitous rise in one parameter value and a corresponding decline in the other value. We will point to the kind of child language data that is needed in order to adjudicate among these competing models.

Timber cross-bracing, Mooloomba House, Point Lookout, North Stradbroke Island

Detail view of timber cross-bracing with polycarbonate sheeting behind as seen from upper level dining studio.

Mooloomba House, Point Lookout, North Stradbroke Island

North elevation, deck below and belvedere above, as seen from path to beach.

South elevation edge, Mooloomba House, Point Lookout, North Stradbroke Island

View along south elevation, stair to belvedere beyond and bedboxes above.

Entrance deck, Mooloomba House, Point Lookout, North Stradbroke Island

View past kitchen windows and roof overhang to entrance deck to the south-west.

View from Mooloomba House, Point Lookout, North Stradbroke Island

View of ocean and coastal vegetation

Timber cross-bracing, Mooloomba House, Point Lookout, North Stradbroke Island

Detail view of timber cross-bracing to dining studio, as seen from upper living area.