Lattice congruences of the weak order

We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the poset of join-irreducibles of the congruence lattice of the poset of regions in terms of certain polyhedral decompositions of the hyperplanes. For a finite Coxeter system (W,S) and a subset K of S, let \eta_K:w \mapsto w_K be the projection onto the parabolic subgroup W_K. We show that the fibers of \eta_K constitute the smallest lattice congruence with 1\equiv s for every s\in(S-K). We give an algorithm for determining the congruence lattice of the weak order for any finite Coxeter group and for a finite Coxeter group of type A or B we define a directed graph on subsets or signed subsets such that the transitive closure of the directed graph is the poset of join-irreducibles of the congruence lattice of the weak order.Comment: 26 pages, 4 figure

Associahedra via spines

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction

Effects of large-scale heathland management on thermal regimes and predation on adders Vipera berus

Management prescriptions for species of conservation concern often focus on creating appropriate habitat conditions, but the spatial scales over which these actions are applied can potentially impact their success. In Northwestern Europe, preventing further loss of lowland heathland through successional changes often involves the mechanical removal of vegetation, creating large blocks of open homogenous habitat. We investigate the influence of this broad-scale habitat management on a heathland specialist, the adder Vipera berus. By deploying temperature loggers and Plasticine adder models in heathland areas with and without complex vegetation cover, we show that (1) cleared areas lack both the temperature variation adders need to thermoregulate effectively and suitable refuges from dangerously high summer temperatures, and (2) attacks by dogs and trampling by grazing livestock are significantly more frequent in cleared areas and closer to footpaths. Habitat management strategies that retain some structural complexity of vegetation within cleared areas, and diverting footpaths away from cleared areas and/or strategic placement of barrier hedging around these areas could potentially reduce the exposure of adders to high predation risk and thermal extremes

Quantitative considerations in Medium Energy Ion Scattering

Due to its unique capability of providing near-quantitative compositional and layer structure information during depth profiling analysis, in favourable cases, with sub-nanometre resolution,medium energy ion scattering (MEIS) is becoming increasingly important to the characterisation of microelectronic device structures in which scaling laws have demanded the growth and doping of layers of nanometre thickness. Here we assess the quantitative accuracy in terms of both depth and concentration, that can be achieved in MEIS depth profiling

Going beyond defining: Preschool educators\u27 use of knowledge in their pedagogical reasoning about vocabulary instruction

Previous research investigating both the knowledge of early childhood educators and the support for vocabulary development present in early childhood settings has indicated that both educator knowledge and enacted practice are less than optimal, which has grave implications for children\u27s early vocabulary learning and later reading achievement. Further, the nature of the relationship between educators\u27 knowledge and practice is unclear, making it difficult to discern the best path towards improved knowledge, practice, and children\u27s vocabulary outcomes. The purpose of the present study was to add to the existing literature by using stimulated recall interviews and a grounded approach to examine how 10 preschool educators used their knowledge to made decisions about their moment-to-moment instruction in support of children\u27s vocabulary development. Results indicate that educators were thinking in highly context-specific ways about their goals and strategies for supporting vocabulary learning, taking into account important knowledge of their instructional history with children and of the children themselves to inform their decision making in the moment. In addition, they reported thinking about research-based goals and strategies for supporting vocabulary learning that went beyond simply defining words for children. Implications for research and professional development are discussed

How to teach fully illiterate adults to read.

About 750 million adults (15%) worldwide lack any literacy skills, most because they lack adequate learning opportunities (UNESCO, 2016). In this chapter, we discuss how to teach to read to such people. We first examine scientific evidence suggesting that literacy acquisition does not radically differ as a function of age of acquisition. We then discuss the data relevant for designing effective methods aimed at teaching literacy to fully illiterate adults. We argue that the available adult data confirm those relative to teaching methods and learning processes that have been gathered on literacy acquisition by children. On the basis of those works we propose principles that should underlie any method aiming at rapidly developing basic literacy skills. Lastly, we present evidence (Kolinsky, Leite, Carvalho, Franco, & Morais, submitted) suggesting that implementing these principles does indeed allow teaching illiterate adults to decode words and pseudo-words in a very short period of time

Subword complexes, cluster complexes, and generalized multi-associahedra

In this paper, we use subword complexes to provide a uniform approach to finite type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any nonnegative integer k, a spherical subword complex called multi-cluster complex. For k=1, we show that this subword complex is isomorphic to the cluster complex of the given type. We show that multi-cluster complexes of types A and B coincide with known simplicial complexes, namely with the simplicial complexes of multi-triangulations and centrally symmetric multi-triangulations respectively. Furthermore, we show that the multi-cluster complex is universal in the sense that every spherical subword complex can be realized as a link of a face of the multi-cluster complex.Comment: 26 pages, 3 Tables, 2 Figures; final versio

Seismicity and Pn Velocity Structure of Central West Antarctica

We have located 117 previously undetected seismic events mainly occurring between 2015 and 2017 that originated from glacial, tectonic, and volcanic processes in central West Antarctica using data recorded on Polar Earth Observing Network (POLENET/ANET) and UK Antarctic Network (UKANET) seismic stations. The seismic events, with local magnitudes (ML) ranging from 1.1 to 3.5, are predominantly clustered in four geographic regions; the Ellsworth Mountains, Thwaites Glacier, Pine Island Glacier, and Mount Takahe. Eighteen of the events are in the Ellsworth Mountains and can be attributed to a mixture of glacial and tectonic processes. The largest event noted in this study was a mid‐crustal (∼19 km focal depth; ML 3.5) normal mechanism earthquake beneath Thwaites Glacier. We also located 91 glacial events near the grounding zones of Thwaites Glacier and Pine Island Glacier that are predominantly associated with time periods of significant calving activity. Eight events, likely arising from volcano‐tectonic processes, occurred beneath Mount Takahe. Using Pn travel times from the seismic events, we find laterally variable uppermost mantle structure in central West Antarctica. On average, the Ellsworth Mountains are underlain by a faster mantle lid (VPn = ∼8.4 km/s) compared to the Amundsen Sea Embayment region (VPn = ∼8.1 km/s). Within the Amundsen Sea Embayment itself, we find mantle lid velocities ranging from ∼8.05 to 8.18 km/s. Laterally heterogeneous uppermost mantle structure, indicative of variable thermal and rheological structure, likely influences both geothermal heat flux and glacial isostatic adjustment spatial patterns and rates within central West Antarctica

Efficacy of language intervention in the early years

Background: Oral language skills in the preschool and early school years are critical to educational success and provide the foundations for the later development of reading comprehension. Methods: In a randomized controlled trial, 180 children from 15 UK nursery schools (n = 12 from each setting; Mage = 4;0) were randomly allocated to receive a 30-week oral language intervention or to a waiting control group. Children in the intervention group received 30 weeks of oral language intervention, beginning in nursery (preschool), in three group sessions per week, continuing with daily sessions on transition to Reception class (pre-Year 1). The intervention was delivered by nursery staff and teaching assistants trained and supported by the research team. Following screening, children were assessed preintervention, following completion of the intervention and after a 6-month delay. Results: Children in the intervention group showed significantly better performance on measures of oral language and spoken narrative skills than children in the waiting control group immediately after the 30 week intervention and after a 6 month delay. Gains in word-level literacy skills were weaker, though clear improvements were observed on measures of phonological awareness. Importantly, improvements in oral language skills generalized to a standardized measure of reading comprehension at maintenance test. Conclusions: Early intervention for children with oral language difficulties is effective and can successfully support the skills, which underpin reading comprehensio