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

Scanning optical pyrometer for measuring temperatures in hollow cathodes

Life-limiting processes in hollow cathodes are determined largely by the temperature of the electron emitter. To support cathode life assessment, a noncontact temperature measurement technique which employs a stepper motor-driven fiber optic probe was developed. The probe is driven inside the hollow cathode and collects light radiated by the hot interior surface of the emitter. Ratio pyrometry is used to determine the axial temperature profile. Thermocouples on the orifice plate provide measurements of the external temperature during cathode operation and are used to calibrate the pyrometer system in situ with a small oven enclosing the externally heated cathode. The diagnostic method and initial measurements of the temperature distribution in a hollow cathode are discussed

Vaccinia virus protein A46R targets multiple Toll-like-interleukin-1 receptor adaptors and contributes to virulence

Viral immune evasion strategies target key aspects of the host antiviral response. Recently, it has been recognized that Toll-like receptors (TLRs) have a role in innate defense against viruses. Here, we define the function of the vaccinia virus (VV) protein A46R and show it inhibits intracellular signalling by a range of TLRs. TLR signalling is triggered by homotypic interactions between the Toll-like-interleukin-1 resistance (TIR) domains of the receptors and adaptor molecules. A46R contains a TIR domain and is the only viral TIR domain-containing protein identified to date. We demonstrate that A46R targets the host TIR adaptors myeloid differentiation factor 88 (MyD88), MyD88 adaptor-like, TIR domain-containing adaptor inducing IFN-beta (TRIF), and the TRIF-related adaptor molecule and thereby interferes with downstream activation of mitogen-activated protein kinases and nuclear factor kappaB. TRIF mediates activation of interferon (IFN) regulatory factor 3 (IRF3) and induction of IFN-beta by TLR3 and TLR4 and suppresses VV replication in macrophages. Here, A46R disrupted TRIF-induced IRF3 activation and induction of the TRIF-dependent gene regulated on activation, normal T cell expressed and secreted. Furthermore, we show that A46R is functionally distinct from another described VV TLR inhibitor, A52R. Importantly, VV lacking the A46R gene was attenuated in a murine intranasal model, demonstrating the importance of A46R for VV virulence

Soluble Host Defense Lectins in Innate Immunity to Influenza Virus

Host defenses against viral infections depend on a complex interplay of innate (nonspecific) and adaptive (specific) components. In the early stages of infection, innate mechanisms represent the main line of host defense, acting to limit the spread of virus in host tissues prior to the induction of the adaptive immune response. Serum and lung fluids contain a range of lectins capable of recognizing and destroying influenza A viruses (IAV). Herein, we review the mechanisms by which soluble endogenous lectins mediate anti-IAV activity, including their role in modulating IAV-induced inflammation and disease and their potential as prophylactic and/or therapeutic treatments during severe IAV-induced disease

What are children's trusts? Early findings from a national survey

<i>Background:</i> The Children Act 2004 and National Service Framework for Children, Young People and Maternity Services require fuller integration of health, education and social services for children and young people in England and Wales. The UK government supported the establishment of 35 experimental children's trust pathfinders (henceforth called children's trusts) in England. <i>Methods:</i> A questionnaire was completed by managers in all 35 children's trusts a year after their start. Children's trust documents were examined. Census and performance indicators were compared between children's trust areas and the rest of England. <i>Results</i> Children's trust areas had demographic and social characteristics typical of England. All children's trusts aimed to improve health, education and social services by greater managerial and service integration. All had boards representing the three sectors; other agencies’ representation varied. Two-thirds of children's trusts had moved towards pooling budgets in at least some service areas. At this stage in their development, some had prioritized joint procurement or provision of services, with formal managerial structures, while others favoured an informal strategic planning, co-ordination and information sharing approach. The commonest priorities for services development were for disabled children (16 children's trusts), followed by early intervention (11) and mental health services (8). <i>Conclusions:</i> The diverse strategies adopted by these 35 children's trusts during their first year is due to their own characteristics and to the way government strategy developed during this period. Whilst some prioritized organizational development, joint financing and commissioning, and information sharing, others laid more emphasis on mechanisms for bringing front-line professionals closer together. Their experiences are of value to others deciding how best to integrate children's services

Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

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

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

Differential binding affinity of mutated peptides for MHC class I is a predictor of survival in advanced lung cancer and melanoma

Background: Cancer mutations generate novel (neo-)peptides recognised by T cells, but the determinants of recognition are not well characterised. The difference in predicted class I major histocompatibility complex (MHC-I) binding affinity between wild-type and corresponding mutant peptides (differential agretopicity index; DAI) may reflect clinically relevant cancer peptide immunogenicity. Our aim was to explore the relationship between DAI, measures of immune infiltration and patient outcomes in advanced cancer. Patients and methods: Cohorts of patients with advanced non-small-cell lung cancer (NSCLC; LUAD, n = 66) and melanoma (SKCM, n = 72) were obtained from The Cancer Genome Atlas. Three additional cohorts of immunotherapy treated patients with advanced melanoma (total n = 131) and NSCLC (n = 31) were analysed. Neopeptides and their clonal status were defined using genomic data. MHC-I binding affinity was predicted for each neopeptide and DAI values summarised as the sample mean DAI. Correlations between mean DAI and markers of immune activity were evaluated using measures of lymphocyte infiltration and immune gene expression. Results: In univariate and multivariate analyses, mean DAI significantly correlated with overall survival in 3/5 cohorts, with evidence of superiority over nonsynonymous mutational and neoantigen burden. In these cohorts, the effect was seen for mean DAI of clonal but not subclonal peptides. In SKCM, the association between mean DAI and survival bordered significance (P = 0.068), reaching significance in an immunotherapy-treated melanoma cohort (P = 0.003). Mean DAI but not mutational nor neoantigen burden was positively correlated with independently derived markers of immune infiltration in both SKCM (P = 0.027) and LUAD (P = 0.024). Conclusions: The association between mean DAI, survival and measures of immune activity support the hypothesis that DAI is a determinant of cancer peptide immunogenicity. Investigation of DAI as a marker of immunologically relevant peptides in further datasets and future clinical studies of neoantigen based immunotherapies is warranted

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