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

Exome capture of Antarctic krill (Euphausia superba) for cost effective genotyping and population genetics with historical collections

Antarctic krill (Euphausia superba Dana) is a keystone species in the Southern Ocean ecosystem, with ecological and commercial significance. However, its vulnerability to climate change requires an urgent investigation of its adaptive potential to future environmental conditions. Historical museum collections of krill from the early 20th century represent an ideal opportunity to investigate how krill have changed over time due to predation, fishing and climate change. However, there is currently no cost-effective method for implementing population scale collection genomics for krill given its genome size (48 Gbp). Here, we assessed the utility of two inexpensive methods for population genetics using historical krill samples, specifically low-coverage shotgun sequencing (i.e. ‘genome-skimming’) and exome capture. Two full-length transcriptomes were generated and used to identify 166 putative gene targets for exome capture bait design. A total of 20 historical krill samples were sequenced using shotgun and exome capture. Mitochondrial and nuclear ribosomal sequences were assembled from both low-coverage shotgun and off-target of exome capture data demonstrating that endogenous DNA sequences could be assembled from historical collections. Although, mitochondrial and ribosomal sequences are variable across individuals from different populations, phylogenetic analysis does not identify any population structure. We find exome capture provides approximately 4500-fold enrichment of sequencing targeted genes, suggesting this approach can generate the sequencing depth required to call identify a significant number of variants. Unlocking historical collections for genomic analyses using exome capture, will provide valuable insights into past and present biodiversity, resilience and adaptability of krill populations to climate change

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