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

Formal and Doctrinal Differences Between Government and Private Contracts

Justice Holmes admonishes us that men must turn square corners when they deal with the Government. This Square Corner Doctrine finds application in the extensive and expanding area of government contracting. This note surveys briefly some ways in which a contract between the United States Government and a private businessman or corporation may be at variance with a contract between private parties based upon common law principles

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

Polyhedral models for generalized associahedra via Coxeter elements

Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A. Zelevinsky associated to each finite type root system a simple convex polytope called \emph{generalized associahedron}. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram. In the first part of this paper, using the parametrization of cluster variables by their $g$-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees with the one given by C. Hohlweg, C. Lange, and H. Thomas in the setup of Cambrian fans developed by N. Reading and D. Speyer.Comment: 31 pages, 2 figures. Changelog: 20111106: initial version 20120403: fixed errors in figures 20120827: revised versio

Steroid Hormone Synthesis by Vaccinia Virus Suppresses the Inflammatory Response to Infection

The 3β-hydroxysteroid dehydrogenase (3β-HSD) isoenzymes play a key role in cellular steroid hormone synthesis. Vaccinia virus (VV) also synthesizes steroid hormones with a 3β-HSD enzyme (v3β-HSD) encoded by gene A44L. Here we examined the effects of v3β-HSD in VV disease using wild-type (vA44L), deletion (vΔA44L), and revertant (vA44L-rev) viruses in a murine intranasal model. Loss of A44L was associated with an attenuated phenotype. Early (days 1–3) after infection with vΔA44L or control viruses the only difference observed between groups was the reduced corticosterone level in lungs and plasma of vΔA44L-infected animals. Other parameters examined (body weight, signs of illness, temperature, virus titres, the pulmonary inflammatory infiltrate, and interferon [IFN]-γ levels) were indistinguishable between groups. Subsequently, vΔA44L-infected animals had reduced weight loss and signs of illness, and displayed a vigorous pulmonary inflammatory response. This was characterized by rapid recruitment of CD4+ and CD8+ lymphocytes, enhanced IFN-γ production and augmented cytotoxic T lymphocyte activity. These data suggest that steroid production by v3β-HSD contributes to virus virulence by inhibiting an effective inflammatory response to infection

A review of overcurrent protection methods for solar photovoltaic DC circuits

This paper investigates the current methodology for overcurrent protection in grid-connected solar photovoltaic (PV) systems. Overcurrent testing procedures for PV modules are examined. The report highlights several shortcomings in the current methodology for overcurrent protection, which may be causing premature module degradation and permanent reduction of generating capacity in PV arrays. A series of recommendations are made for improvements to the relevant guidelines and standards

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

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

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