Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

Estimating and evaluating the statistics of gapped local-alignment scores

We present a novel maximum-likelihood-based algorithm for estimating the distribution of alignment scores from the scores of unrelated sequences in a database search. Using a new method for measuring the accuracy of p-values, we show that our maximum-likelihood-based algorithm is more accurate than existing regression-based and lookup table methods. We explore a more sophisticated way of modeling and estimating the score distributions (using a two-component mixture model and expectation maximization), but conclude that this does not improve significantly over simply ignoring scores with small E-values during estimation. Finally, we measure the classification accuracy of p-values estimated in different ways and observe that inaccurate p-values can, somewhat paradoxically, lead to higher classification accuracy. We explain this paradox and argue that statistical accuracy, not classification accuracy, should be the primary criterion in comparisons of similarity search methods that return p-values that adjust for target sequence length.

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitary operations. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.

History and nomenclature of the theropod dinosaur tracks Bueckeburgichnus and Megalosauripus

The most recent account of Bueckeburgichnus maximus Kuhn 1958, a distinctive theropod dinosaur track from the Lower Cretaceous of Germany, is shown to be based on a referred specimen mistakenly identified as the holotype and the correct name of this taxon is deemed to be Megalosauripus maximus (Kuhn 1958). This minor revision has important consequences for nomenclature of the many European, Asian, North American and Australian dinosaur tracks attributed to megalosaurian theropods. Many of those tracks were named Megalosauripus, but that name has a confusing multiplicity of meanings and it should be restricted to the highly characteristic dinosaur track formerly identified as Bueckeburgichnus. Other tracks named "Megalosauripus”; (in its several other senses) will require new nomenclature, despite their extensive and repeated revision since 1996. It is recommended that future revision should adopt conventions of the International Code of Zoological Nomenclature. Although previous revisions expressed an intention to adhere to those conventions, these were not put into practice, with the unfortunate result of multiplying the problems that surround the nomenclature of megalosaur tracks. Introduction of the name Megalosauripus maximus (Kuhn 1958) eliminates those burgeoning problems and permits the introduction of new and objective nomenclature for presumed megalosaur tracks.

Recording and preserving legal history

The lack of a systematic approach in Australia to recording and preserving legal history was highlighted in the article by Catherine Hutchins in the August 2002 issue of the Australian Bar Review. This article describes the modest, albeit continuing, efforts on the part of the Supreme Court Library to meet this need in the State of Queensland. The efforts began in 1983 and have recently escalated with a series of exhibitions, talks, displays, interviews and preservations of documents (from online publication).

Fluid-mobile trace element constraints on the role of slab melting and implications for Archaean crustal growth models

We use published and new trace element data to identify element ratios which discriminate between arc magmas from the supra-subduction zone mantle wedge and those formed by direct melting of subducted crust (i.e. adakites). The clearest distinction is obtained with those element ratios which are strongly fractionated during refertilisation of the depleted mantle wedge, ultimately reflecting slab dehydration. Hence, adakites have significantly lower Pb/Nd and B/Be but higher Nb/Ta than typical arc magmas and continental crust as a whole. Although Li and Be are also overenriched in continental crust, behaviour of Li/Yb and Be/Nd is more complex and these ratios do not provide unique signatures of slab melting. Archaean tonalite-trondhjemite-granodiorites (TTGs) strongly resemble ordinary mantle wedge-derived arc magmas in terms of fluid-mobile trace element content, implying that they-did not form by slab melting but that they originated from mantle which was hydrated and enriched in elements lost from slabs during prograde dehydration. We suggest that Archaean TTGs formed by extensive fractional crystallisation from a mafic precursor. It is widely claimed that the time between the creation and subduction of oceanic lithosphere was significantly shorter in the Archaean (i.e. 20 Ma) than it is today. This difference was seen as an attractive explanation for the presumed preponderance of adakitic magmas during the first half of Earth's history. However, when we consider the effects of a higher potential mantle temperature on the thickness of oceanic crust, it follows that the mean age of oceanic lithosphere has remained virtually constant. Formation of adakites has therefore always depended on local plate geometry and not on potential mantle temperature.

'Why does cultural studies want history?'

Cultural studies has often been accused of maintaining too strong a focus on the contemporary and the immediate as a result of its primary interest in popular culture and the media. The role of history, such criticisms suggest, has been displaced by this contemporary emphasis. Nonetheless, much cultural studies work takes a principled stand on the necessity of historicising the products of its research. Consequently, it is worth asking, with British historian Carolyn Steedman--'why does cultural studies want history?' This article begins to answer that question through the discussion of some aspects of a specific research project within Australian cultural studies.

When social psychology became less social: Prasad and the history of rumor research

Rumor research, in general, and its delayed incorporation of the work, of rumor researcher Jamuna Prasad, in particular, exemplify how the intellectual climate of American social psychology discouraged the development of social approaches. In the present paper, we explain his conceptualization of how rumors start and spread, and explore findings from subsequent research supporting or negating his propositions. It is our contention that, although Prasad had identified the basic variables involved in rumor generation and transmission correctly, mainstream social psychological research in the 1940s did not incorporate his contributions. Instead, mirroring the Zeitgeist of American social psychology, rumor research was approached from a predominantly individual level of analysis. In the present paper, the authors have tried to resurrect some of the group-level variables from Prasad's treatment of rumor and to suggest that social psychology adopt a more 'social' approach to rumor.