Bounds on the diameter of Cayley graphs of the symmetric group

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.Comment: 17 pages, 6 table

Dissolution susceptibility of glass-like carbon versus crystalline graphite in high-pressure aqueous fluids and implications for the behavior of organic matter in subduction zones

Organic matter, showing variable degrees of crystallinity and thus of graphitization, is an important source of carbon in subducted sediments, as demonstrated by the isotopic signatures of deep and ultra-deep diamonds and volcanic emissions in arc settings. In this experimental study, we investigated the dissolution of sp2 hybridized carbon in aqueous fluids at 1 and 3 GPa, and 800\ub0C, taking as end-members i) crystalline synthetic graphite and ii) X-ray amorphous glass-like carbon. We chose glass-like carbon as an analogue of natural \u201cdisordered\u201d graphitic carbon derived from organic matter, because unlike other forms of poorly ordered carbon it does not undergo any structural modification at the investigated experimental conditions, allowing approach to thermodynamic equilibrium. Textural observations, Raman spectroscopy, synchrotron X-ray diffraction and dissolution susceptibility of char produced by thermal decomposition of glucose (representative of non-transformed organic matter) at the same experimental conditions support this assumption. The redox state of the experiments was buffered at \u394FMQ 48 \u20130.5 using double capsules and either fayalite-magnetite-quartz (FMQ) or nickel-nickel oxide (NNO) buffers. At the investigated P\u2013T\u2013fO2 conditions, the dominant aqueous dissolution product is carbon dioxide, formed by oxidation of solid carbon. At 1 GPa and 800\ub0C, oxidative dissolution of glass-like carbon produces 16\u201319 mol% more carbon dioxide than crystalline graphite. In contrast, fluids interacting with glass-like carbon at the higher pressure of 3 GPa show only a limited increase in CO2 (fH2NNO) or even a lower CO2 content (fH2FMQ) with respect to fluids interacting with crystalline graphite. The measured fluid compositions allowed retrieving the difference in Gibbs free energy (\u394G) between glass-like carbon and graphite, which is +1.7(1) kJ/mol at 1 GPa\u2013800\ub0C and +0.51(1) kJ/mol (fH2NNO) at 3 GPa\u2013800\ub0C. Thermodynamic modeling suggests that the decline in dissolution susceptibility at high pressure is related to the higher compressibility of glass-like carbon with respect to crystalline graphite, resulting in G\u2013P curves crossing at about 3.4 GPa at 800\ub0C, close to the graphite\u2013diamond transition. The new experimental data suggest that, in the presence of aqueous fluids that flush subducted sediments, the removal of poorly crystalline \u201cdisordered\u201d graphitic carbon is more efficient than that of crystalline graphite especially at shallow levels of subduction zones, where the difference in free energy is higher and the availability of poorly organized metastable carbonaceous matter and of aqueous fluids produced by devolatilization of the downgoing slab is maximized. At depths greater than 110 km, the small differences in \u394G imply that there is minimal energetic drive for transforming \u201cdisordered\u201d graphitic carbon to ordered graphite; \u201cdisordered\u201d graphitic carbon could even be energetically slightly favored in a narrow P interval

Learning to look : evaluating the student experience of an interactive image appraisal activity

Introduction: Student radiographers have expressed difficulty in performing image appraisal tasks. The purpose of this study was to investigate the value of a workshop delivered to level 4 undergraduate students. All students completed an image appraisal activity, inputting their appraisal into software that displayed their response alongside an expert opinion. They were asked to identify and discuss any discrepancy. Methods: All Level 4 students participated in an image appraisal workshop and were subsequently invited to take part in a focus group immediately after the activity. Twenty-three students took part in three focus groups (n = 7; n = 8; n = 8). A thematic analysis of transcripts was performed alongside validation from observations during the image appraisal activity. Results: Findings demonstrate that despite teaching and resources being available, students had focused on learning a generic checklist for image appraisal, had not appreciated the application of projection specific criteria and felt underprepared. The use of specific criteria and repetition within the task was considered useful. They identified learning needs and misconceptions through peer discussion and via the expert opinion, highlighting the value of feedback. Students enjoyed the workshop and made suggestions for implementation into the curriculum. Conclusion: Educators must not assume that the provision of resources will result in students developing deep knowledge. Teaching and learning strategies that are task specific are recommended to avoid a surface approach to learning. Time, repetition and appropriate feedback are essential to enable learners to develop competence and confidence for complex visual tasks, such as image appraisal

Statistical Language Modelling

Grammar-based natural language processing has reached a level where it can `understand' language to a limited degree in restricted domains. For example, it is possible to parse textual material very accurately and assign semantic relations to parts of sentences. An alternative approach originates from the work of Shannon over half a century ago [41], [42]. This approach assigns probabilities to linguistic events, where mathematical models are used to represent statistical knowledge. Once models are built, we decide which event is more likely than the others according to their probabilities. Although statistical methods currently use a very impoverished representation of speech and language (typically finite state), it is possible to train the underlying models from large amounts of data. Importantly, such statistical approaches often produce useful results. Statistical approaches seem especially well-suited to spoken language which is often spontaneous or conversational and not readily amenable to standard grammar-based approaches

Real-time data assimilative modeling on Georges bank

Real-time oceanic forecasts were constructed at sea on Georges Bank during Spring 1999. Ship- and shore-based computations were combined to deliver daily 3-day forecasts to shipboard scientists for interpreting observations and planning operations. Data assimilated included acoustic Doppler current profiler velocities, drifter trajectories, and taxa-specific plankton observations from a Video Plankton Recorder (VPR) system. Services provided included basic 3-D circulation forecasts, forecast positions of drifters, dye and zoo-plankton, and the advective adjustment of observations to produce synoptic maps. The results indicate that real-time, at-sea data assimilative modeling can provide valuable information services and can be deployed routinely, provided that networking among ships, instruments, and shore continues to improve. This paper summarizes the real-time modeling experience. Results of the larger effort including scientific data interpretation are being reported separately