The triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

We study the Ising model on the triangular lattice with nearest-neighbor couplings $K_{\rm nn}$, next-nearest-neighbor couplings $K_{\rm nnn}>0$, and a magnetic field $H$. This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case $K_{\rm nn}<0$, but we also explore the ferromagnetic regime $K_{\rm nn}\ge 0$ for H=0. For $K_{\rm nn}<0$ and H=0 we locate a critical phase presumably covering the whole range $-\infty < K_{\rm nn}<0$. For $K_{\rm nn}<0$, $H\neq 0$ we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit $H \to \infty$ this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential

On Saturating Sets in Small Projective Geometries

AbstractA set of points, S⊆PG(r, q), is said to be ϱ -saturating if, for any point x∈PG(r, q), there exist ϱ+ 1 points in S that generate a subspace in which x lies. The cardinality of a smallest possible set S with this property is denoted by k(r, q,ϱ ). We give a short survey of what is known about k(r, q, 1) and present new results for k(r, q, 2) for small values of r and q. One construction presented proves that k(5, q, 2) ≤ 3 q+ 1 forq= 2, q≥ 4. We further give an upper bound onk (ϱ+ 1, pm, ϱ)

Orbifold instantons, moment maps, and Yang-Mills theory with sources

We revisit the problem of constructing instantons on ADE orbifolds R4/Γ and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R4/Γ which are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kähler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically symmetric Γ-equivariant connections on complex V bundles over R4/Γ which are tailored to the way in which the orbifold group acts on the fibers. Some explicit Abelian and non-Abelian SU(2)-invariant solutions to the instanton equations on the orbifold are worked out. © 2013 American Physical Society

Wâhkôhtowin: the governance of good community-academic research relationships to improve the health and well-being of children in Alexander First Nation

Community-based participatory research (CBPR) is a promising decolonizing approach to health and social sciences research with First Nation Peoples. In CBPR, the use of a community advisory committee can act as an anchoring site for trusting reciprocal relationships, collaborative decision-making, and co-learning and co-creation. Through a qualitative case study, this article illustrates the collective experiences of a well-established, multidisciplinary, and intersectoral committee that reviews, monitors, and guides multiple research projects in a First Nation community in Canada. Participants of the Alexander Research Committee (ARC) share examples of the value of fostering a high level of commitment to building both positive working relationships and learning spaces that ultimately result in research and policy impacts for their community

The chronology and kinematics of late Palaeozoic deformation in the NW contact metamorphic aureole of the Land's End Granite

A structural investigation of coastal exposures between Cape Cornwall and Pendeen Watch, in the NW contact metamorphic aureole of the Land’s End Granite, has confirmed a similar deformation chronology as in a reference section around Porthleven. D1 deformation is represented by an ubiquitous bedding-parallel S1 cleavage although F1 folds have not been recognised. D2 deformation is more localised and characterised by open F2 folds that verge WSW to NW and are associated with an ENE to SE dipping S2 crenulation cleavage. These structures are commonly obscured by later deformation and contact metamorphism and have not been described previously. A set of steeply inclined NNW-SSE trending, and subordinate set of moderately SE dipping, post-D2 metamorphic quartz veins formed coevally during an episode of strike-slip deformation prior to, or during, the early stages of D3 deformation. D3 deformation is widespread and represented by F3 folds and a WNW to NW dipping S3 crenulation cleavage; it has been recorded previously as D2 deformation. Two orders of F3 folds are developed; first order folds have a wavelength of up to 50 m, verge ESE, and result in vertical or steeply inclined bedding and S1 cleavage on their short limbs. Second order folds usually have a wavelength of 1 m or less and usually verge ESE, unless on the short limb of first order folds, where they verge WNW. Previously published data, indicating a dominant NW to WNW vergence of F3 folds on the northern flank of the Land’s End Granite are incorrect. D3 structures are consistent with formation during the extensional reactivation of large-scale thrust faults. Granite emplacement post-dates all three episodes of ductile deformation but granites and their host rocks are deformed by a late brittle expression of D3 deformation. The Land’s End pluton has been accommodated, at the current exposure level, primarily by roof uplift that has resulted in the tilting of D3 and earlier structures to the NW by 40-50º; this may have been accompanied by differential vertical axis rotations of the host rock. The last significant Palaeozoic deformation episode formed F4 folds and S4 cleavage and was a consequence of Mid- to Late Permian ENE-WSW shortening

A discrete Laplace-Beltrami operator for simplicial surfaces

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace-Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay triangulations of piecewise flat surfaces revised and expanded. References added. Some minor changes, typos corrected. v3: fixed inaccuracies in discussion of flip algorithm, corrected attributions, added references, some minor revision to improve expositio

Teacher interventions in small group work in secondary mathematics and science lessons

Collaborative problem solving, when students work in pairs or small groups on a curriculum-related task, has become an increasingly common feature of classroom education. This paper reports a study of a topic which has received relatively little attention: how teachers can most usefully intervene when students are working in a group, but have encountered some sort of problem. The data used comes from a large scale interventional study of mathematics and science teaching in secondary schools in south east England, in which interactions between teachers and students were recorded in their usual classrooms. We identify the typical problem situations which lead to teachers’ interventions, and describe the different ways teachers were observed to intervene. We examine the different types of intervention, and consider how effective they are in helping group work proceed in a productive manner. Finally, we offer some conclusions about the practical implications of these findings.This is the final version of the article. It was first available from Taylor & Francis via http://dx.doi.org/10.1080/09500782.2015.112536

Multiparameter flow cytometry for the characterisation of extracellular markers on human mesenchymal stem cells

Extracellular surface proteins are used to identify fully-functional human mesenchymal stem cells (hMSCs) in a mixed population. Here, a multiparameter flow cytometry assay was developed to examine the expression of several bone marrow-derived hMSC markers simultaneously at the single cell level. The multiparameter approach demonstrates a depth of analysis that goes far beyond the conventional single or dual staining methods. CD73, CD90 and CD105 were chosen as positive markers as they are expressed on multipotent hMSCs, whilst CD34 and HLA-DR were chosen as negative indicators. Single colour analysis suggested a population purity of 100 %; in contrast, when analysed via the multiparameter method, the CD73/CD105/CD90/HLA-DR/CD34 phenotypes represented 94.5 ± 1.3 % of the total cell population. Also, although CD271 has been posited as a definite early stage hMSC marker, here we show it is not present on pre-passage cells, highlighting the need for careful marker selection. © 2013 Springer Science+Business Media Dordrecht

Evaluating invasion risk for freshwater fishes in South Africa

South Africa, as a signatory of the Convention on Biological Diversity, has an obligation to identify, prioritise and manage invasive species and their introduction pathways. However, this requires knowledge of the introduction pathways, factors influencing establishment success, invasive potential, current distributions and ecological impacts. Objectives: To evaluate the Fish Invasiveness Screening Kit (FISK) to predict the invasion risk posed by fish species proposed for introduction into South Africa. Method: FISK assessments were compiled for species whose invasion status in South Africa was known. A Receiver operating characteristic (ROC) analysis was conducted to calibrate the FISK for South Africa. The calibrated FISK was used to evaluate the risk that three species recently proposed for importation for aquaculture could become invasive in South Africa. Results: A FISK score of 14 was identified as the threshold to delineate between species that could become invasive in South Africa and those that are unlikely to become invasive. Of the three species evaluated, Silurus glanis had a high risk of becoming invasive in South Africa, Lates calcarifer was likely to be invasive and Oncorhynchus tshawytscha was unlikely to be invasive in South Africa. Conclusion: FISK was demonstrated to be a useful risk assessment tool to evaluate the invasion risk posed by species proposed for use in aquaculture. For the large number of fish imported for the pet trade, a rapid screening assessment to flag potentially high risk species was recommended prior to a full FISK assessment for flagged species.EM201