Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt

The effect of topography on the steady-state wind and buoyancy-driven Subtropical Gyre

This paper studies the impact of topography and increased vertical resolution on steady-state wind and buoyancy-driven circulation in the Subtropical Gyre. Buoyancy driving is represented by mass exchange across the interface separating layers of constant density. The mass exchange in turn is parameterized in terms of the departure of a layer thickness from a reference value. A 2-layer ocean model is developed that incorporates topography that depends on the meridional co-ordinate, and the problem reduces to solving a first order partial differential equation governing the upper layer inverse planetary potential vorticity. Two distinct families of characteristic curves are required to span the entire subtropical gyre; an interior family emanating from the eastern boundary and a family lying in the northwestern corner that begin and end along the oceanic edge of the western boundary current. It is demonstrated that when the ocean shoals (deepens) poleward, the area of the recirculating gyre in the northwestern corner decreases (increases) in response to the increased (decreased) phase speed of long baroclinic Rossby waves. The model is applied to the subtropical North Atlantic gyre, using climatological Ekman pumping, zonally averaged topography and a realistic representation of the eastern boundary and the solutions are qualitatively compared with these from a general ocean circulation model. To address how increased vertical resolution modifies the recirculating gyre structure, solutions are calculated for a 3-layer flat bottom ocean model. The circulation in the top and bottom layers of this model are qualitatively similar to those in the 2-layer model. In the middle layer there is a recirculating anticyclonic gyre of extent similar to that in the 2-layer model. Outside this gyre is a second anticyclonic gyre of larger horizontal extent. The double-gyre structure in the middle layer is associated with the existence of two separatrices subdividing the layers into three regions. These curves separate two distinct families of characteristic curves each associated with the upper and lower layer inverse planetary potential vorticity equations

Developing a Pedagogical Framework for Designing a Multisensory Serious Gaming Environment

The importance of multisensory interaction for learning has increased with improved understanding of children’s sensory development, and a flourishing interest in embodied cognition. The potential to foster new forms of multisensory interaction through various sensor, mobile and haptic technologies is promising in providing new ways for young children to engage with key mathematical concepts. However, designing effective learning environments for real world classrooms is challenging, and requires a pedagogically, rather than technologically, driven approach to design. This paper describes initial work underpinning the development of a pedagogical framework, intended to inform the design of a multisensory serious gaming environment. It identifies the theoretical basis of the framework, illustrates how this informs teaching strategies, and outlines key technology research driven perspectives and considerations important for informing design. An initial table mapping mathematical concepts to design, a framework of considerations for design, and a process model of how the framework will continue to be developed across the design process are provided

Embodied truths: How dynamic gestures and speech contribute to mathematical proof practices

Grounded and embodied theories of cognition suggest that both language and the body play crucial roles in grounding higher-order thought. This paper investigates how particular forms of speech and gesture function together to support abstract thought in mathematical proof construction. We use computerized text analysis software to evaluate how speech patterns support valid proof construction for two different tasks, and we use gesture analysis to investigate how dynamic gestures—those gestures that depict and transform mathematical objects—further support proof practices above and beyond speech patterns. We also evaluate the degree to which speech and gesture convey distinct information about mathematical reasoning during proving. Dynamic gestures and speech indicating logical inference support valid proof construction, and both dynamic gestures and speech uniquely predict variance in valid proof construction. Thus, dynamic gestures and speech each make separate and important contributions to the formulation of mathematical arguments, and both modalities can convey elements of students’ understanding to teachers and researchers

Hyperthyroidism and human chorionic gonadotrophin production in gestational trophoblastic disease

Background: Gestational trophoblastic disease (GTD) is a rare complication of pregnancy, ranging from molar pregnancy to choriocarcinoma. Patients with persistent disease require treatment with chemotherapy. For the vast majority, prognosis is excellent. Occasionally, GTD is complicated by hyperthyroidism, which may require treatment. This is thought to occur due to molecular mimicry between human chorionic gonadotrophin (HCG) and thyroid-stimulating hormone (TSH), and hence cross-reactivity with the TSH receptor. Hyperthyroidism usually resolves as the GTD is successfully treated and correspondingly HCG levels normalise. Methods: This paper reviews cases of GTD treated over a 5-year period at one of the three UK centres and identifies the prevalence of hyperthyroidism in this population. Four cases with clinical hyperthyroidism are discussed. Results: On review of the 196 patients with gestational trophoblastic neoplasia treated with chemotherapy in Sheffield since 2005, 14 (7%) had biochemical hyperthyroidism. Of these, four had evidence of clinical hyperthyroidism. Conclusion: Concomitant biochemical thyroid disease in patients with GTD is relatively common, and measurement of thyroid function in patients with persistent GTD is, therefore, important. The development of hyperthyroidism is largely influenced by the level of HCG and disease burden, and usually settles with treatment of the persistent GTD. However, rarely the thyroid stimulation can have potentially life-threatening consequences

The SOLAS air-sea gas exchange experiment (SAGE) 2004

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 58 (2011): 753-763, doi:10.1016/j.dsr2.2010.10.015.The SOLAS air-sea gas exchange experiment (SAGE) was a multiple-objective study investigating gas-transfer processes and the influence of iron fertilisation on biologically driven gas exchange in high-nitrate low-silicic acid low-chlorophyll (HNLSiLC) Sub-Antarctic waters characteristic of the expansive Subpolar Zone of the southern oceans. This paper provides a general introduction and summary of the main experimental findings. The release site was selected from a pre-voyage desktop study of environmental parameters to be in the south-west Bounty Trough (46.5°S 172.5°E) to the south-east of New Zealand and the experiment conducted between mid-March and mid-April 2004. In common with other mesoscale iron addition experiments (FeAX’s), SAGE was designed as a Lagrangian study quantifying key biological and physical drivers influencing the air-sea gas exchange processes of CO2, DMS and other biogenic gases associated with an iron-induced phytoplankton bloom. A dual tracer SF6/3He release enabled quantification of both the lateral evolution of a labelled volume (patch) of ocean and the air-sea tracer exchange at the 10’s of km’s scale, in conjunction with the iron fertilisation. Estimates from the dual-tracer experiment found a quadratic dependency of the gas exchange coefficient on windspeed that is widely applicable and describes air-sea gas exchange in strong wind regimes. Within the patch, local and micrometeorological gas exchange process studies (100 m scale) and physical variables such as near-surface turbulence, temperature microstructure at the interface, wave properties, and wind speed were quantified to further assist the development of gas exchange models for high-wind environments. There was a significant increase in the photosynthetic competence (Fv/Fm) of resident phytoplankton within the first day following iron addition, but in contrast to other FeAX’s, rates of net primary production and column-integrated chlorophyll a concentrations had only doubled relative to the unfertilised surrounding waters by the end of the experiment. After 15 days and four iron additions totalling 1.1 tonne Fe2+, this was a very modest response compared to the other mesoscale iron enrichment experiments. An investigation of the factors limiting bloom development considered co- limitation by light and other nutrients, the phytoplankton seed-stock and grazing regulation. Whilst incident light levels and the initial Si:N ratio were the lowest recorded in all FeAX’s to date, there was only a small seed-stock of diatoms (less than 1% of biomass) and the main response to iron addition was by the picophytoplankton. A high rate of dilution of the fertilised patch relative to phytoplankton growth rate, the greater than expected depth of the surface mixed layer and microzooplankton grazing were all considered as factors that prevented significant biomass accumulation. In line with the limited response, the enhanced biological draw-down of pCO2 was small and masked by a general increase in pCO2 due to mixing with higher pCO2 waters. The DMS precursor DMSP was kept in check through grazing activity and in contrast to most FeAX’s dissolved dimethylsulfide (DMS) concentration declined through the experiment. SAGE is an important low-end member in the range of responses to iron addition in FeAX’s. In the context of iron fertilisation as a geoengineering tool for atmospheric CO2 removal, SAGE has clearly demonstrated that a significant proportion of the low iron ocean may not produce a phytoplankton bloom in response to iron addition.SAGE was jointly funded through the New Zealand Foundation for Research, Science and Technology (FRST) programs (C01X0204) "Drivers and Mitigation of Global Change" and (C01X0223) "Ocean Ecosystems: Their Contribution to NZ Marine Productivity." Funding was also provided for specific collaborations by the US National Science Foundation from grants OCE-0326814 (Ward), OCE-0327779 (Ho), and OCE 0327188 OCE-0326814 (Minnett) and the UK Natural Environment Research Council NER/B/S/2003/00282 (Archer). The New Zealand International Science and Technology (ISAT) linkages fund provided additional funding (Archer and Ziolkowski), and the many collaborator institutions also provided valuable support