Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy

Blanks, a nuclear siRNA/dsRNA-binding complex component, is required for Drosophila spermiogenesis

Small RNAs and a diverse array of protein partners control gene expression in eukaryotes through a variety of mechanisms. By combining siRNA affinity chromatography and mass spectrometry, we have identified the double-stranded RNA-binding domain protein Blanks to be an siRNA- and dsRNA-binding protein from Drosophila S2 cells. We find that Blanks is a nuclear factor that contributes to the efficiency of RNAi. Biochemical fractionation of a Blanks-containing complex shows that the Blanks complex is unlike previously described RNA-induced silencing complexes and associates with the DEAD-box helicase RM62, a protein previously implicated in RNA silencing. In flies, Blanks is highly expressed in testes tissues and is necessary for postmeiotic spermiogenesis, but loss of Blanks is not accompanied by detectable transposon derepression. Instead, genes related to innate immunity pathways are up-regulated in blanks mutant testes. These results reveal Blanks to be a unique component of a nuclear siRNA/dsRNA-binding complex that contributes to essential RNA silencing-related pathways in the male germ line

Berenstein-Zelevinsky triangles, elementary couplings and fusion rules

We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page

Evaluating techniques for sampling stream crayfish (paranephrops planifrons)

We evaluated several capture and analysis techniques for estimating abundance and size structure of freshwater crayfish (Paranephrops planifrons) (koura) from a forested North Island, New Zealand stream to provide a methodological basis for future population studies. Direct observation at night and collecting with baited traps were not considered useful. A quadrat sampler was highly biased toward collecting small individuals. Handnetting at night and estimating abundances using the depletion method were not as efficient as handnetting on different dates and analysing by a mark-recapture technique. Electrofishing was effective in collecting koura from different habitats and resulted in the highest abundance estimates, and mark-recapture estimates appeared to be more precise than depletion estimates, especially if multiple recaptures were made. Handnetting captured more large crayfish relative to electrofishing or the quadrat sampler

ROM-based quantum computation: Experimental explorations using Nuclear Magnetic Resonance, and future prospects

ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of writable qubits). Here we consider a number of small (one and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using NMR ensemble QC. The average fidelities for the implementation were in the ranges 0.9 - 0.97 for the one-qubit algorithms, and 0.84 - 0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature ``real-world'' problem relating to the lengths of paths in a network.Comment: 11 pages, 5 figure

Submerged in the mainstream? A case study of an immigrant learner in a New Zealand primary classroom

Immigrant children from diverse language backgrounds face not only linguistic challenges when enrolled in mainstream English-medium classrooms, but also difficulties adjusting to an unfamiliar learning community. The culture of primary school classrooms in New Zealand typically reflects conventions across three dimensions: interactional, instructional task performance and cognitive-academic development. All three dimensions are underpinned by the culturally specific discourse conventions involved in language socialisation. New learners may be helped by classmates or their teacher to understand and successfully use these conventions, but left on their own they may sink rather than swim. This is a case study of one Taiwanese 11-year old boy, 'John', who entered a New Zealand primary classroom midway through the school year. John's basic conversational ability was sound, but he did not possess the interactive classroom skills needed to operate in the new culture of learning. Selected from a wider study of the classroom, transcript data from audio-recorded excerpts of John's interactions over several months with his teacher and classmates are interpreted from perspectives derived from sociocultural and language socialisation theories. The article concludes with a brief consideration of the extent to which John constructed, or was constrained from constructing meaningful learning experiences, and suggestions for further research and reflection

Speech rhythm: a metaphor?

Is speech rhythmic? In the absence of evidence for a traditional view that languages strive to coordinate either syllables or stress-feet with regular time intervals, we consider the alternative that languages exhibit contrastive rhythm subsisting merely in the alternation of stronger and weaker elements. This is initially plausible, particularly for languages with a steep ‘prominence gradient’, i.e. a large disparity between stronger and weaker elements; but we point out that alternation is poorly achieved even by a ‘stress-timed’ language such as English, and, historically, languages have conspicuously failed to adopt simple phonological remedies that would ensure alternation. Languages seem more concerned to allow ‘syntagmatic contrast’ between successive units and to use durational effects to support linguistic functions than to facilitate rhythm. Furthermore, some languages (e.g. Tamil, Korean) lack the lexical prominence which would most straightforwardly underpin prominence alternation. We conclude that speech is not incontestibly rhythmic, and may even be antirhythmic. However, its linguistic structure and patterning allow the metaphorical extension of rhythm in varying degrees and in different ways depending on the language, and that it is this analogical process which allows speech to be matched to external rhythms

Brewing of filter coffee

We report progress on mathematical modelling of coffee grounds in a drip filter coffee machine. The report focuses on the evolution of the shape of the bed of coffee grounds during extraction with some work also carried out on the chemistry of extraction. This work was sponsored by Philips who are interested in understanding an observed correlation between the final shape of the coffee grounds and the quality of the coffee. We used experimental data gathered by Philips and ourselves to identify regimes in the coffee brewing process and relevant regions of parameter space. Our work makes it clear that a number of separate processes define the shape of the coffee bed depending on the values of the parameters involved e.g. the size of the grains and the speed of fluid flow during extraction. We began work on constructing mathematical models of the redistribution of the coffee grounds specialised to each region and on a model of extraction. A variety of analytic and numerical tools were used. Furthermore our research has progressed far enough to allow us to begin to exploit connections between this problem and other areas of science, in particular the areas of sedimentology and geomorphology, where the processes we have observed in coffee brewing have been studied

The threshold hypothesis revisited: bilingual lexical knowledge and non-verbal IQ development

The threshold hypothesis (Cummins 1976 et passim) is one of the most influential theoretical frameworks on the relation between bilingualism and cognition. The aim of our study is to contribute towards an operationalisation of the threshold hypothesis. We analyse data from 100 Turkish-English successive bilingual children and from their parents, and investigate the relation between bilingualism and cognition. When compared with monolingual control groups, the bilinguals in our study have smaller vocabulary sizes in both languages. However, when both vocabularies are taken together and the total conceptual vocabulary is computed no bilingual disadvantage can be identified. Children with parental support for L1 outperform the monolingual control groups in our study in terms of non-verbal intelligence scores. The originality of the present study resides in the fact that, to our knowledge, for the first time parental support for L1 and dominance in L1 is linked to the cognitive development of the children